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Topology:
General Topology 2021
Clark Barwick
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Contents
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Front Matter
1
Subspaces of Euclidean space
Basic definitions
Continuity
Connectedness
Problem set 1, due 5 October 2021
Problem set 2, due 19 October 2021
2
Abstract topological spaces
Topologies
Continuity
Specifying topologies efficiently
Quotient spaces
Problem set 3, due 2 November 2021
Products
Problem set 4, due 16 November 2021
3
Compactness
Compact topological spaces
Compact Hausdorff topological spaces
The Tikhonov Theorem
Problem set 5, due 4 December 2021
4
Separation
Trennungsaxiome
Urysohn & Tietze
5
Elements of set theory
Sets and elements
Bounded comprehension
Unions
Ordered pairs
Maps
Bijections
Products and sets of maps
Injections and surjections
The algebra of subsets
Inverse and direct image
Products of sets
Coproducts of sets
Back Matter
Authored in PreTeXt
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Chapter
3
Compactness
3.1
Compact topological spaces
3.2
Compact Hausdorff topological spaces
3.3
The Tikhonov Theorem
3.4
Problem set 5, due 4 December 2021