Graduate syllabus; undergraduate syllabus
Office hours: MW 2--5, TR 2--3, S 2--4 at LBV 321
Email: david.milovich@tamiu.edu
Textbook: Topology by James R. Munkres; ISBN 9780134689517
Old exams.
Spring 2015 course materials

Day Readings Topics Photos Other HW HW due
on Day 		Revision
due on Day
1 1,2 logic; sets; functions zip pdf 5 12
2 3,5 relations; products zip pdf 7 13
3 7,9,10 countability; choice;
well orderings 		zip countability
notes (pdf) 		pdf 8 15
4 10,12,13 SΩ; topologies; bases zip pdf 9 16
5 14--16 order, product, and
subspace topologies 		zip alphabets
(pdf) 		pdf 10 17
6 17 closed sets; convergence;
Hausdorff spaces 		zip a closure
proof (pdf) 		pdf 11 18
7 18 continuous functions zip pdf 12 19
8 18,19 homeomorphisms;
infinite products 		zip pdf 13 20
9 20,21 the metric topology zip pdf 15 22
10 21,22 metrizability;
quotient maps 		zip pdf 16 23
11 22--24 quotient topology;
connectedness 		zip pdf 17 24
12 23,24 connectedness;
compactness introduction 		zip compactness in
terms of chains (pdf) 		pdf 18 24
13 26--27 compactness zip pdf 19 24
14 26--27 compactness zip pdf 20 24
15 27--29 compactness zip The UCT: a sequential
approach (pdf) 		pdf 21 24
16 30 countability axioms zip Why RR is not Lindelof pdf 22
17 31, 32 separation axioms zip Separation axiom
preservation chart (pdf) 		pdf 23
18 31, 32 separation axioms zip π-Base pdf 24
19 33 Urysohn's Lemma zip pdf 24
20 34 Urysohn's metrization theorem;
Cech embedding 		zip pdf 24
21 11, 37, 38 Stone-Cech compactification;
Zorn's Lemma; Tychonoff Theorem 		zip Alexander Subbase
Lemma (pdf) 		pdf 24
22 43--45.1 complete metric spaces;
a space-filling curve 		zip Hilbert curve
The UCT: a sequential
approach (again) (pdf) 		pdf 24
23 Q&A pdf
24 Q&A zip
Final Exam (6:00, May 9)
Plan ahead: the syllabus schedule covers the full semester.