Lecture(s)  

Sections (approximately)    

Comments/Topics

1

1.2, 1.3

Sets, operations on sets

1

1.4, 1.5

Indexed families of sets, arbitrary unions and products

1

1.6, 1.7

Functions, relations

1

2.1, 2.2

Metric spaces

1

2.3

Continuity

1

2.4

Open balls

1

2.5

Limits

1

2.6, 2.7

Open sets, closed sets, subsets, equivalence

1

3.2

Topological spaces

1

Munkres

Basis of a topology

1

Munkres

Closure, interior, boundary

1

3.6

Subspaces

1

3.5

Functions, continuity, homeomorphism

1

3.7

Products

1

Halloween Lecture

Scary topologies

1

3.8

Quotient topologies

1

4.2, 4.3

Connectedness, connectedness of the real line

1

4.5, 4.6

Components, path connectedness, contractibility

1

5.2

Compactness

1

5.3

Compact subsets of the real line

1

5.4

Products of compact spaces

1

5.5

Compact metric spaces

1

various

Heine Borel Theorem

various

various

Surfaces