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Topology
MATH 342 Spring 2026
Kyle Ormsby
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Front Matter
1
Course Documents
1.1
Syllabus
Course Information
2
Course Notes
2.1
Week 1
Monday
Welcome to the Generous Arena
So what is a topology?
Examples of topologies
Wednesday
Continuity
Topological properties
Building continuous functions
Friday
2.2
Week 2
Monday
Topology from the categorical viewpoint
Categories
Functors
Wednesday
More on functors
New topologies from old
The subspace topology
Friday
The quotient topology
2.3
Week 3
Monday
Real projective space
Pushouts
Wednesday
Pushouts in Top
Categorical products and the product topology
Friday
2.4
Week 4
Monday
Separation of points
Wednesday
Closure and limit points
Sequences and limits
Sequences, closure, and continuity
Friday
A first glimpse of compactness
2.5
Week 5
Monday
Compactness via topological induction
Inheritance of compactness
Separation of disjoint compact subspaces
Wednesday
Friday
3
Homework
3.1
Homework 01
3.2
Homework 02
3.3
Homework 03
3.4
Homework 04
Chapter
2
Course Notes
These course notes should provide a full description of what we cover in class, but they are not a substitute for attending class. In particular, there will be a number of activities, diagrams, and discussions that cannot be replicated in text.
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If you find any typos or errors in the notes, please post your observation to the #notes channel in our
Zulip workspace
.
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2.1
Week 1
2.2
Week 2
2.3
Week 3
2.4
Week 4
2.5
Week 5
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