Learn · An invitation to Topology
Lecture 5 of 74week-01
mod01lec05 - Functions
Prof. Indrava Roy · IMSc
Credits and licence
- From
- An invitation to Topology, IMSc (at NPTEL)
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge. Coordinated by IIT Madras.
- Who can watch
- Tweens profiles and older. How courses are placed
All the lectures
- mod01lec01 - Introduction to Topology
- mod01lec02 - Basic Set theory
- mod01lec03 - Mathematical Logic - Part 1
- mod01lec04 - Mathematical Logic - Part 2
- mod01lec05 - Functions
- mod01lec06 - Finite Sets - Part 1
- mod01lec07 - Finite Sets - Part 2
- mod01lec08 - Infinite Sets
- mod01lec09 - Infinite Sets and Axiom of Choice
- mod02lec10 - Definition of aTopology
- mod02lec11 - Examples of different topologies:
- mod02lec12 - Basis for a topology
- mod02lec13 - Various topologies on the real line
- mod02lec14 - Comparison of topologies - Part 1 : Finer and coarser topologies
- mod02lec15 - Comparison of topologies - Part 2: Comparing the various topologies on R
- mod02lec16 - Basis and Sub-basis for a topology
- mod03lec17 - Various topologies: the subspace topology
- mod02lec18 - The Product topology
- mod02lec19 - Topologies on arbitrary Cartesian products
- mod02lec20 - Metric topology - Part 1
- mod03lec21 - Metric topology - Part 2
- mod03lec22 - Metric topology - Part 3
- mod04lec23 - Closed Sets
- mod04lec24 - Closure and Limit points
- mod04lec25 - Continuous functions
- mod04lec26 - Construction of continuous functions
- mod04lec27 - Continuous functions on metric spaces - Part 1
- mod04lec28 - Continuous functions on metric spaces - Part 2
- mod05lec29 - Connectedness
- mod05lec30 - Some conditions for Connectedness
- mod05lec31 - Connectedness of the Real Line
- mod05lec32 - Connectedness of a Linear Continuum
- mod05lec33 - The Intermediate Value Theorem
- mod06lec34 - Path-connectedness
- mod06lec35 - Connectedness does not imply Path-connectedness - Part 1
- mod06lec36 - Connectedness does not imply Path-connectedness - Part 2
- mod06lec37 - Connected and Path-connected Components
- mod06lec38 - Local connectedness and Local Path-connectedness
- mod07lec39 - Compactness
- mod07lec40 - Properties of compact spaces
- mod07lec41 - The Heine-Borel Theorem
- mod07lec42 - Tychonoff't theorem
- mod07lec43 - Proof of Tychonoff's theorem - Part 1
- mod07lec44 - Proof of Tychonoff's theorem - Part 2
- mod08lec45 - Compactness in metric spaces
- mod08lec46 - Lebesgue Number Lemma and the Uniform Continuity theorem
- mod08lec47 - Different Kinds of Compactness
- mod08lec48 - Equivalence of various compactness properties for Metric Spaces
- mod08lec49 - Compactness and Sequential Compactness in arbitrary topological spaces
- mod09lec50 - Baire Spaces
- mod09lec51 - Properties and Examples of Baire Spaces
- mod09lec52 - The Baire Category Theorem
- mod09lec53 - Complete Metric Spaces and the Baire Category theorem - Part 1
- mod09lec54 - Complete Metric Spaces and the Baire Category theorem - Part 2
- mod09lec55 - Application of the Baire Category theorem
- mod10lec56 - Regular and Normal spaces
- mod10lec57 - Properties and examples of regular and normal spaces
- mod10lec58 - Urysohn's Lemma
- mod10lec59 - Proof of Urysohn's Lemma
- mod10lec60 - Tietze Extension theorem - Part 1
- mod10lec61 - Tietze Extension theorem - Part 2
- mod11lec62 - Compactness and Completeness in Metric spaces
- mod11lec63 - The space of continuous functions - Part 1
- mod11lec64 - The space of continuous functions - Part 2
- mod11lec65 - Equicontinuity
- mod11lec66 - Total boundedness and Equicontinuity - Part 1
- mod11lec67 - Total boundedness and Equicontinuity - Part 2
- mod12lec68 - Topology of compact convergence - Part 1
- mod12lec69 - Topology of compact convergence - Part 2
- mod12lec70 - Equicontinuity revisited - Part 1
- mod12lec71 - Equicontinuity revisited - Part 2
- mod12lec72 - Locally compact Hausdorff spaces
- mod12lec73 - The Arzelà - Ascoli theorem
- Live Session 04-05-2022