Schedule

This is the tentative course schedule; there may be small changes as the semester progresses. We plan to cover selected topics from Chapter 1-3 of the textbook. We review selected topics of basic set theory in chapter 1, and then we jump to Chapter 2. We will review topics in Chapter 1 later if needed.

Week 1 (Week of Jan 15)

First day of class: Wednesday, Jan 17.

Sections and topics covered:

§ 7: Countable and Uncountable Sets

Week 2 (Week of Jan 22)

Sections and topics covered:

§ 7: Countable and Uncountable Sets

§ 12: Topological Spaces

Week 3 (Week of Jan 29)

Sections and topics covered:

§ 12: Topological Spaces

§ 13: Basis for a Topology

§ 14: The Order Topology

Week 4 (Week of Feb 5)

Sections and topics covered:

§ 15: The Product Topology on \(X\times Y\)

§ 16: The Subspace Topology

Week 5 (Week of Feb 12)

Sections and topics covered:

§ 16: The Subspace Topology

§ 17: The Closed Sets and Limit Points

§ 18: Continuous Functions

Week 6 (Week of Feb 19)

Sections and topics covered:

§ 18: Continuous Functions

Week 7 (Week of Feb 26)

Sections and topics covered:

§ 20: The Metric Topology

Week 8 (Week of Mar 4)

Sections and topics covered:

§ 20: The Metric Topology

Week 9 (Week of Mar 11)

SPRING BREAK (March 11- March 15).

Week 10 (Week of Mar 18)

Sections and topics covered:

§ 20: The Metric Topology

§ 21: The Metric Topology (continued)

Week 11 (Week of Mar 25)

Sections and topics covered:

§ 23: Connected Spaces

§ 24: Connected Spaces of the Real Line

Week 12 (Week of Apr 1)

Sections and topics covered:

§ 26: Compact Spaces

Week 13 (Week of Apr 8)

Sections and topics covered:

§ 27: Compact Spaces of the Real Line

Week 14 (Week of Apr 15)

Sections and topics covered:

§ 27: Compact Spaces of the Real Line

§ 28: Limit Point Compactness

Week 15 (Week of Apr 22)

Sections and topics covered:

§ 43: Complete Metric Spaces

§ 44: A Space-Filling Curve

Week 16 (Week of Apr 29)

Sections and topics covered:

Review