Lec 55: Statement and proof of Open Mapping Theorem
★
★
★
★
☆
4/5
Tuit catalog
Synthesis notes of video analyses, assessed and condensed, in French and English.
55,839 tuit
·
974 channels
·
42 domains
·
Last update: Nov 10, 2026
Agriculture & Food
172
AI — Models & Research
4626
AI — News & Applications
2241
AI & Society
1273
Archaeology
143
Arts & Architecture
1496
Astronomy & Cosmology
3722
Biology
2220
Chemistry
353
Climate & Ecology
1105
Computing & Cybersecurity
4535
Control & Robotics
393
Earth Sciences & Geography
306
Economics & Finance
4039
Education
796
Energy
1572
Engineering & Technology
3452
Foresight & Science Fiction
345
Geopolitics & Defence
596
History
785
Hobbies & Practical
465
Language & Linguistics
324
Law & Justice
594
Literature & Writing
978
Mathematics
2391
Media & Information
307
Medicine & Health
3235
Neuroscience
446
Paleontology
102
Personal Development
1207
Philosophy & Ethics
888
Physics
3634
Politics & Institutions
756
Psychology
668
Religion & Beliefs
258
Science — General & History
1882
Society & Culture
1202
Space Exploration
959
Sports
96
Transport & Mobility
229
Urban Planning & Mobility
102
Video Games
946
JMP
Abnormal psychology
24
VSC
Advice on careers and achieving success
141
TRP
Aerospace and aviation technology
937
PBF
Algebra
267
PBMW
Algebraic geometry
159
PBPD
Algebraic topology
81
UMB
Algorithms and data structures
84
KNBT
Alternative and renewable energy industries
137
THV
Alternative and renewable energy sources and technology
180
MKJD
Alzheimer’s, dementia, Parkinson’s disease and other neurodegenerative diseases
68
QDHA
Ancient Greek and Roman philosophy
52
NHC
Ancient history
36
JBFU
Animals and society
24
PBW
Applied mathematics
20
TTB
Applied optics
46
NKDS
Archaeological sites
36
NK
Archaeology
43
NKD
Archaeology by period
31
AM
Architecture
34
UYQD
Artificial general intelligence (AGI)
52
UYQ
Artificial intelligence (AI)
2240
LNQH
Artificial intelligence law and regulations
22
NHF
Asian history
20
VSPM
Assertiveness, motivation, self-esteem and positive mental attitude
478
TTDS
Astronautics
997
PGG
Astronomical observation: observatories, equipment and methods
116
PG
Astronomy, space and time
919
PHVB
Astrophysics
122
PHM
Atomic and molecular physics
75
MKJA
Autism Spectrum Disorder
20
TJFM
Automatic control engineering
71
TRC
Automotive technology and trades
34
TRPS
Aviation skills and piloting
22
KFFK
Banking
23
THYB
Battery technology
204
PBTB
Bayesian inference
32
PSB
Biochemistry
313
RNCB
Biodiversity
37
PSAD
Bioethics
40
DNBH
Biography: historical, political and military
84
DNBM
Biography: philosophy and social sciences
20
DNBR
Biography: royalty
26
DNBT
Biography: science, technology and medicine
83
DNBL
Biography: writers
40
PS
Biology, life sciences
30
MQW
Biomedical engineering
24
PHVN
Biophysics
30
TCB
Biotechnology
63
TNK
Building construction and materials
35
TNKE
Building physics and energy-efficient construction
20
KJ
Business and Management
59
KJJ
Business and the environment; sustainable approaches to business
43
KJG
Business ethics and social responsibility
21
KJD
Business innovation
49
KJC
Business strategy
60
PBKA
Calculus
44
PBK
Calculus and mathematical analysis
66
MJD
Cardiovascular medicine
38
JNR
Careers guidance
38
PSAN1
Cellular and molecular neuroscience
23
PSF
Cellular biology (cytology)
135
JPQB
Central
65
PN
Chemistry
29
MJCL2
Chemotherapy
26
JMC
Child, developmental and lifespan psychology
32
AMVD
City and town planning: architectural aspects
33
NHWR3
Civil wars
23
PHD
Classical mechanics
197
RNPG
Climate change
235
RBPC
Climatology and climate modelling
40
MBGR1
Clinical trials
25
UTC
Cloud computing
35
GPJ
Coding theory and cryptology
42
JMR
Cognition and cognitive psychology
142
PSAN5
Cognitive and behavioural neuroscience
248
GTK
Cognitive studies
40
NHTW
Cold wars and proxy conflicts
20
PBV
Combinatorics and graph theory
55
GTC
Communication studies
36
TJK
Communications engineering
42
DSM
Comparative literature
23
LNCH
Competition law
29
PBKD
Complex analysis, complex variables
60
PSAX
Computational biology
109
KNTV
Computer and video game industry
228
UYF
Computer architecture and logic design
126
URH
Computer fraud and hacking
295
UDX
Computer games
659
UGG
Computer games design
243
UK
Computer hardware
84
UYM
Computer modelling and simulation
23
UT
Computer networking and communications
27
UY
Computer science
72
UR
Computer security
769
URJ
Computer viruses, Trojans and worms
32
UYQV
Computer vision
122
PHFC
Condensed matter physics (liquid state and solid state physics)
140
RNKH
Conservation of wildlife and habitats
32
JBGX
Conspiracy theories
54
LNDX
Constitution
32
VFJB3
Coping with
21
KFFH
Corporate finance
30
JPZ
Corruption in politics, government and society
33
PGK
Cosmology and the universe
1052
CBV
Creative writing and creative writing guides
21
JKVF
Criminal investigation and detection
43
GPH
Data science and analysis
40
UN
Databases
20
GTS
Decolonisation of knowledge
50
KCM
Development economics and emerging economies
67
GTP
Development studies
43
PSC
Developmental biology
41
MBNH3
Dietetics and nutrition
28
PBMP
Differential and Riemannian geometry
42
PBKJ
Differential calculus and equations
97
UBJ
Digital and information technologies: social and ethical aspects
1267
UB
Digital and Information technology: general topics
64
UXA
Digital Humanities
50
UD
Digital Lifestyle and online world: consumer and user guides
32
KCVM
Digital or internet economics
67
WNA
Dinosaurs and the prehistoric world: general interest
72
JPSD
Diplomacy
38
JBFM
Disability: social aspects
27
JBCT5
Disinformation and misinformation
76
KJDD
Disruptive innovation
29
ATFR
Documentary films
23
RNFD
Drought and water supply
26
PHDT
Dynamics and statics
82
QDHC
East Asian and Indian philosophy
30
PSAF
Ecological science, the Biosphere
53
KCX
Economic and financial crises and disasters
43
KCA
Economic theory and philosophy
35
KC
Economics
22
JN
Education
28
JNDH
Education: examinations and assessment
31
JNK
Educational administration and organization
21
JNV
Educational equipment and technology, computer-aided learning (CAL)
77
JNC
Educational psychology
29
JNF
Educational strategies and policy
30
JPHF
Elections and referenda
50
TRV
Electric vehicles
98
THR
Electrical engineering
71
KNBL
Electrical power generation and distribution industries
280
PHK
Electricity, electromagnetism and magnetism
279
TJFD
Electronic devices and materials
258
TJFC
Electronics: circuits and components
190
PHDB
Elementary mechanics
38
VSPQ
Emotions and emotional intelligence
28
MJG
Endocrinology
24
PHDY
Energy
26
LNCR
Energy and natural resources law
39
THYC
Energy efficiency
70
KNB
Energy industries and utilities
224
RNFY
Energy resources
55
THY
Energy, power generation, distribution and storage
390
TGMB
Engineering thermodynamics
25
TBC
Engineering: general
23
TGMF
Engineering: Mechanics of fluids
23
TGMD
Engineering: Mechanics of solids
24
UFL
Enterprise software
59
KJH
Entrepreneurship
199
KCVG
Environmental economics
109
MBNH2
Environmental factors
51
RND
Environmental policy and protocols
205
RNA
Environmentalist thought and ideology
81
MBNS
Epidemiology and Medical statistics
127
SXE
eSports
25
QDTQ
Ethics and moral philosophy
52
PSVP
Ethology and animal behaviour
39
PBMH
Euclidean geometry
44
NHD
European history
27
PSAJ
Evolution
179
PSXE
Evolutionary anthropology
92
UYQE
Expert systems
27
JPFQ
Far-right political ideologies and movements
20
ATFG
Film guides and reviews
110
ATFA
Film history, theory or criticism
46
ATFN
Film: styles and genres
342
KFF
Finance and the finance industry
37
KFFF
Financial technology (fintech)
36
RNFF
Food security and supply
38
PBKF
Functional analysis and transforms
32
PGM
Galaxies and stars
346
UMK
Games development and programming
45
JBSF
Gender studies, gender groups
27
JBSF1
Gender studies: women and girls
103
MKZV
Gene therapy
41
GTZ
General studies and General knowledge
36
UYQF
Generative artificial intelligence
2603
TCBG
Genetic engineering
51
PSAK
Genetics (non-medical)
654
RBG
Geology, geomorphology and the lithosphere
28
PBM
Geometry
22
PHVG
Geophysics
41
JPSL
Geopolitics
328
THVG
Geothermal energy and power
37
PHDV
Gravity
34
KFFS
Green finance
59
PBG
Groups and group theory
105
MJF
Haematology
21
MBP
Health systems and services
39
JBFN
Health, illness or addiction: social aspects
24
VFMD
Health: Diets and nutrition
24
TNKH
Heating, lighting, ventilation
24
MJJ
Hepatology
40
JNM
Higher education, tertiary education
248
RBGF
Historical geology and palaeogeology
51
NHAH
Historiography
35
NH
History
41
AGA
History of art
40
UBB
History of Computing, digital and information technologies
57
TBX
History of engineering and technology
31
JBCC9
History of ideas
20
PBX
History of mathematics
43
NHQ
History of other geographical groupings and regions or specific cultures
27
PDX
History of science
163
KJZ
History of specific companies
39
NHK
History of the Americas
56
NHT
History: specific events and topics
28
JBFD
Housing and homelessness
22
PSX
Human biology
27
JPVH
Human rights, civil rights
44
THD
Hydrogen technologies
63
THVH
Hydropower
25
TTBM
Imaging systems and technology
26
MJCM
Immunology
101
PDR
Impact of science and technology on society
126
AMB
Individual architects and architectural firms
32
AGB
Individual artists, art monographs
35
ATFB
Individual film directors, film-makers
31
PDG
Industrial applications of scientific research and technological innovation
55
MJCJ
Infectious and contagious diseases
55
KNTX
Information technology industries
405
JWD
Information warfare
32
PSVA2
Insects (entomology)
22
GTV
Institutions and learned societies: general
34
PBKL
Integral calculus and equations
29
GT
Interdisciplinary studies
22
KCL
International economics
21
JPSN
International institutions
28
JPS
International relations
25
KCLT
International trade and commerce
55
ATN
Internet and digital media: arts and performance
53
UDB
Internet guides and online services
26
UBW
Internet: general works
42
JMHC
Interpersonal communication and skills
30
DNPB
Interviews
46
TBY
Inventions and inventors
21
KFFM
Investment and securities
149
KJMV3
IT and information systems management
41
VSCB
Job hunting
29
KCF
Labour
97
PHJL
Laser physics
50
TTBL
Laser technology and holography
22
PSA
Life sciences: general issues
22
ULJL
Linux
23
DSRC
Literary companions, book reviews and guides
36
DSBB
Literary studies: ancient, classical and medieval
23
DSK
Literary studies: fiction, novelists and prose writers
77
DSB
Literary studies: general
26
DSC
Literary studies: poetry and poets
50
DSA
Literary theory
30
UYQM
Machine learning
1194
UKPM
Macintosh
22
KCB
Macroeconomics
23
KJMB
Management: leadership and motivation
70
PSPM
Marine biology
24
NHTM
Maritime history
34
TGM
Materials science
55
MKCM
Materno-foetal medicine
41
PHU
Mathematical
179
PBCD
Mathematical logic
114
PBWH
Mathematical modelling
54
UYA
Mathematical theory of computation
259
PB
Mathematics
173
MFKH3
Maturation and ageing
78
JBCT
Media studies
26
JBCT1
Media studies: internet, digital media and society
71
JBCT4
Media studies: journalism
90
MBPM
Medical administration and management
23
MBF
Medical and health informatics
67
MFN
Medical genetics
181
MKS
Medical imaging
21
MBGL
Medical laboratory testing and techniques
21
PHVD
Medical physics
20
MBGR
Medical research
60
MB
Medicine
24
RBPM
Meteorology
39
PSG
Microbiology (non-medical)
66
JBFH
Migration, immigration and emigration
34
JWK
Military and defence strategy
47
NHWR9
Military history: post-WW2 conflicts
20
VSPD
Mindfulness
21
TTU
Mining technology and engineering
22
UMS
Mobile and handheld device programming
24
TJKT1
Mobile phone technology
26
UDT
Mobile phones and smartphones: consumer
60
PSD
Molecular biology
185
KCBM
Monetary economics
82
JNAM
Moral and social purpose of education
24
WGCB
Motor cars: general interest
27
GLZ
Museology and heritage studies
54
TBN
Nanotechnology
34
UYX
Natural computing
908
RNR
Natural disasters
27
UYQL
Natural language and machine translation
157
WN
Nature and the natural world: general interest
47
UTN
Network security
63
UTP
Networking standards and protocols
27
UYQN
Neural networks and fuzzy systems
460
MKJ
Neurology and clinical neurophysiology
58
PSAN
Neurosciences
127
KNTP2
News media and journalism
24
PNRL
Nuclear chemistry, photochemistry and radiation
27
RNQ
Nuclear issues
31
MKR
Nuclear medicine
66
PHN
Nuclear physics
115
THK
Nuclear power and engineering
219
PBH
Number theory
191
PBKS
Numerical analysis
41
MQC
Nursing
24
MQCA
Nursing fundamentals and skills
39
RBKC
Oceanography (seas and oceans)
59
MJCL
Oncology
132
KJSG
Online marketing
33
MJQ
Ophthalmology
22
PHJ
Optical physics
179
PBU
Optimization
33
TTMW
Ordnance, weapons technology
22
PNN
Organic chemistry
67
RBX
Palaeontology
102
MKB
Palliative medicine
37
UYFP
Parallel processing
27
PHP
Particle and high-energy physics
147
GTU
Peace studies and conflict resolution
42
MBNH
Personal and public health
23
UKP
Personal computers
27
VSB
Personal finance
56
UDA
Personal organization software and apps
22
KJMV2
Personnel and human resources management
40
KNBP
Petroleum, oil and gas industries
96
MKG
Pharmacology
74
QD
Philosophy
47
JNA
Philosophy and theory of education
41
PBB
Philosophy of mathematics
33
QDTM
Philosophy of mind
86
PDA
Philosophy of science
155
QDTK
Philosophy: epistemology and theory of knowledge
129
QDTL
Philosophy: logic
47
QDTJ
Philosophy: metaphysics and ontology
42
PNR
Physical chemistry
72
PH
Physics
200
PHDF
Physics: Fluid mechanics
55
JMM
Physiological psychology, neuropsychology, biopsychology
26
MFG
Physiology
54
PSTB
Plant biology
32
PHFP
Plasma physics
34
JPW
Political activism
22
KCP
Political economy
129
WHB
Political humour
23
JPHL
Political leaders and leadership
45
JPL
Political parties and party platforms
21
JPA
Political science and theory
32
JPH
Political structure and processes
26
JPHV
Political structures
47
JP
Politics and government
69
RNP
Pollution and threats to the environment
43
PDZM
Popular and recreational mathematics
116
WNX
Popular astronomy and space
813
VFD
Popular medicine and health
25
QDX
Popular philosophy
21
QDXB
Popular philosophy: Meaning of life
31
VSP
Popular psychology
272
PDZ
Popular science
455
JBFC
Poverty and precarity
21
JPWG
Pressure groups, protest movements and non-violent action
36
URD
Privacy and data protection
39
PBT
Probability and statistics
259
TDCX
Process engineering technology and techniques
21
TGP
Production and industrial engineering
45
UMX
Programming and scripting languages: general
119
UMA
Programming techniques
38
JMAF
Psychoanalytical and Freudian psychology
24
JMA
Psychological theory, systems, schools and viewpoints
26
JM
Psychology
72
JMQ
Psychology: emotions
29
JMT
Psychology: states of consciousness
40
JMS
Psychology: the self, ego, identity, personality
29
MKGW
Psychopharmacology
39
JPP
Public administration
41
KFFD
Public finance and taxation
50
MBN
Public health and preventive medicine
79
GPSD
Quantitative research methods
20
PHQ
Quantum physics (quantum mechanics and quantum field theory)
1012
JBFA1
Racism and racial discrimination
32
PBKB
Real analysis, real variables
42
MFGG
Regional physiology
25
PHR
Relativity physics
349
QRAM2
Religion and politics
23
QRAM3
Religion and science
27
DNP
Reportage, journalism or collected columns
76
GPS
Research methods
103
RNKH2
Restoration ecology
21
NHTV
Revolutions, uprisings, rebellions
24
TJFM1
Robotics
322
KJS
Sales and marketing
50
KJMV7
Sales and marketing management
46
UFLS
SAP (Systems, applications and products in databases)
24
FLU
Science fiction: aliens
77
FLW
Science fiction: space exploration
200
FLS
Science fiction: space opera
35
PDK
Science funding and policy
70
PD
Science: general issues
65
PDM
Scientific research
63
WNCS1
Sea life and the seashore: general interest
25
NHWR7
Second World War
61
VS
Self-help, personal development and practical advice
32
CFG
Semantics, discourse analysis, stylistics
33
GTD
Semiotics
65
PSAN4
Sensory and motor systems
23
PBCH
Set theory
20
TJKH
Signal processing
35
NHTS
Slavery, enslaved persons and abolition of slavery
28
JHMC
Social and cultural anthropology
22
NHTB
Social and cultural history
80
JBF
Social and ethical issues
36
QDTS
Social and political philosophy
85
JBFX
Social attitudes
22
JBFZ
Social forecasting, future studies
46
RNT
Social impact of environmental issues
50
JMH
Social, group or collective psychology
81
CFB
Sociolinguistics
38
VSS
Soft skills and dealing with other people
25
UMZ
Software Engineering
100
UMZT
Software testing and verification
32
THVS
Solar power
221
PGS
Solar system: the Sun and planets
340
TTDX
Space exploration
547
TTD
Space science
278
CBP
Speaking in public: advice and guides
26
DNS
Speeches
45
PHS
Statistical physics
77
PBWL
Stochastics
52
RNU
Sustainability
63
TVF
Sustainable agriculture
25
JNU
Teaching of a specific subject
30
TB
Technology: general issues
28
ATJ
Television
41
ATJS
Television: styles and genres
20
ATD
Theatre studies
26
PGC
Theoretical and mathematical astronomy
77
AMA
Theory of architecture
26
ABA
Theory of art
55
AVA
Theory of music and musicology
25
PHH
Thermodynamics and heat
35
PGZ
Time (chronology), time systems and standards
47
PBP
Topology
41
RPT
Transport planning and policy
22
RPC
Urban and municipal planning and policy
70
UYZG
User interface design and usability
21
MBNK
Vaccination
31
RBC
Volcanology and seismology
38
RNH
Waste management
21
PHDS
Wave mechanics (vibration and acoustics)
43
UGB
Web graphics and design
24
UMW
Web programming
97
JKSB
Welfare and benefit systems
21
WNCF
Wildlife: mammals: general interest
29
THVW
Wind power
32
CBW
Writing and editing guides
28
PSV
Zoology and animal sciences
22
Lec 55: OFDM Capacity
★
★
★
★
☆
4/5
Lec 54: Capacity of a Gaussian Channels
★
★
★
★
☆
4/5
Lec 53: Capacity of a DMCs
★
★
★
★
☆
4/5
Lec 52: Channel Capacity
★
★
★
★
☆
4/5
Lec 51: OFDM
★
★
★
★
☆
4/5
Lec 50: Channel Estimation
★
★
★
★
☆
4/5
Lec 49: MMSE equalization II
★
★
★
★
☆
4/5
Lec 45: Mini-LED Device Fabrication and Applications
★
★
★
★
☆
4/5
Lec 44: Light-Emitting Characteristics of LEDs
★
★
★
★
☆
4/5
Lec 43: Fundamentals of LEDs
★
★
★
★
☆
4/5
Lec 42: MiniLEDs-Backlight Technology
★
★
★
★
☆
4/5
Lec 41: Autostereoscopic & Advanced 3D Displays
★
★
★
★
☆
4/5
Lec 35: Facial Animation & Deformation
★
★
★
★
☆
4/5
Lec 34: Keyframing & Character Animation
★
★
★
★
☆
4/5
Lec 33: Animation Principles
★
★
★
★
☆
4/5
Le ZEvent explose, OpenAI inquiète, Méta et Google répliquent, et NVidia épate
ZEvent explodes, OpenAI worries, Meta and Google respond, and Nvidia impresses
★
★
★
☆
☆
3/5
Le piège Copilot : vous payez pour prendre du retard.
The Copilot Trap: You’re Paying to Fall Behind.
★
★
★
★
☆
4/5
Le moment où le métier de développeur a basculé
The moment when the developer profession shifted
★
★
★
★
☆
4/5
Le Grand Debunk de la Santé 1 - Olivier Hertel, idée reçue "Les vaccins provoquent l'autisme"
The Great Health Debunk 1 - Olivier Hertel, common misconception "Vaccines cause autism"
★
★
★
★
☆
4/5
Le Grand Debunk de la Santé 1 - Dr Bruno Raynard, idée reçue "Jeûner permet de soigner le cancer"
The Great Health Debunk 1 - Dr. Bruno Raynard, common myth: "Fasting can cure cancer"
★
★
★
★
☆
4/5
La Mafia del Alcohol - Te esconde la Verdad.
The Alcohol Mafia - Hides the Truth from You.
★
★
★
★
☆
4/5
iPhone ULTRA et voitures VOLANTES : Mes 20 Produits coups de coeurs de L'IFA 2026
iPhone ULTRA and FLYING cars: My 20 favorites from IFA 2026
★
★
★
☆
☆
3/5
I Went OFF Grid for 48 Hours… Here’s What Happened
★
★
★
☆
☆
3/5
Guide Onimusha Action - 04 - Labo Souterrain - Grand Nue
Onimusha Action Guide - 04 - Underground Lab - Grand Nue
★
★
★
☆
☆
3/5
GPT‑6 Astra vient-il de franchir le seuil de l’AGI ?
Has GPT-6 Astra just crossed the AGI threshold?
★
★
★
★
☆
4/5
GPT 6 Astra is a freak
★
★
★
★
☆
4/5