General Topology (Point Set Topology)
22 videos
This is intended as an undergraduate-level, first-semester, General Topology course. We begin with Set Theory, and work our way through the three Cs of Topology (Continuity, Connectedness, and Compactness). The course is a continuation of my Logic playlist, and so it starts with Set Theory and a review of Relations and Functions, then gets into Topology proper starting on Lecture 5. Logic playlist: https://www.youtube.com/playlist?list=PLJWhXkxQzDF58EHPCuxHS-iaMpom9qTqg
Resources
- 1
Axiomatic Set Theory – Lecture 1 (Topology)
1:50:40
- 2
Axiomatic Set Theory & Intro to Topology – Lecture 2 (Topology)
2:10:29
- 3
Set Theoretical Relations – Lecture 3 (Topology)
2:11:42
- 4
Relations and Functions – Lecture 4 (Topology)
1:53:37
- 5
Functions & Open Sets in a Topology – Lecture 5 (Topology)
1:45:56
- 6
Open Sets – Lecture 6 (Topology)
1:54:52
- 7
Basis for a Topology – Lecture 7 (Topology)
2:08:54
- 8
Basis for a Topology – Lecture 8 (Topology)
1:44:27
- 9
Closed Sets – Lecture 9 (Topology)
1:58:44
- 10
Interior and Closure of Sets – Lecture 10 (Topology)
1:53:44
- 11
Limit Points & Boundaries – Lecture 11 (Topology)
2:05:52
- 12
Subspace & Product Topologies – Lecture 12 (Topology)
1:54:34
- 13
Product and Quotient Space Topologies – Lecture 13 (Topology)
2:05:01
- 14
Continuity and the Epsilon-Delta Definition – Lecture 14 (Topology)
2:05:39
- 15
Continuity & Homeomorphisms – Lecture 15 (Topology)
2:32:39
- 16
Metric Spaces – Lecture 16 (Topology)
1:50:16
- 17
Properties of Metric Spaces & Isometries – Lecture 17 (Topology)
1:34:32
- 18
Connected Topological Spaces – Lecture 18 (Topology)
1:47:10
- 19
Connectedness, Homeomorphisms, & IVT – Lecture 19 (Topology)
1:42:58
- 20
Intermediate Value Theorem, Path Connected, & Compactness– Lecture 20 (Topology)
1:41:25
- 21
Compactness & Open Covers – Lecture 21 (Topology)
1:17:25
- 22
Compactness & Extreme Value Theorem: Last Lecture! – Lecture 22 (Topology)
1:00:38