Math 4710 & 5710 Fall 2014
Tentative Schedule


August

Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday


1
2


3
4
5
6
7
8
9


10
11
12
13
14
15
16


17
18
19
Class 1
21
Class 2
23


24
Class 3
26
Class 4
28
Class 5
30


31





September

Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday


No Class
2
Class 6
4
Class 7
6


7
Class 8
9
Class 9
11
Class 10
13


14
Class 11
16
Class 12
18
Class 13
20


21
Class 14
23
Class 15
25
Class 16
27


28
Class 17
30





October

Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday


Class 18
2
Class 19
4


5
Class 20
7
Class 21
9
Class 22
11


12
Class 23
14
Class 24
No Class
No Class
18


19
Class 25
21
Class 26
23
Class 27
25


26
Class 28
28
Class 29
30
Class 30





November

Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday


1


2
Class 31
4
Class 32
6
Class 33
8


9
Class 34
11
Class 35
13
Class 36
15


16
Class 37
18
Class 38
20
Class 39
22


23
Class 40
25
No Class
No Class
No Class
29


30





December

Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday


Class 41
2
Class 42
4
Class 43
6


7
8
9
10
11
Final Exam
MAT 4710
3-5:30
13


14
15
16
17
18
19
20


21
22
23
24
25
26
27


28
29
30
31







Class # Topic (what we've actually done)...

 Syllabus and "What is Topology?"
 Set theory basics some functions
 More functions and start relations
 Characteristic functions, power sets, & total orders
 Equivalence relations/partitions, dictionary order, & infinite cartesian products
 Dedekind cut and Cauchy sequence constructions of the reals & well ordering
 Cardinality and the Continuum Hypothesis
 More cardinality & ZFC
 Statements equivalent to AC (like Zorn's lemma)
 Catch up & Review
 Set Test
 Introduction to Topological Spaces (Section 12)
 Bases (Section 13)
 The lower limit and K-topologies on R and began order topologies (Sections 13-14)
 Order, product, and subspace topologies (Sections 14-16)
 Finish subspace topologies. Closed sets (Sections 16-17)
 Closure & limit points (Section 17)
 Hausdorff spaces & Continuity (Section 18)
 Continuity (Section 18)
 Homeomorphisms and more continuity (Section 18)
 Product vs. box topologies (Section 19)
 Metric spaces (Section 20)
 More metric examples (uniform metric)
 Metrizability and Metric continuity = Topological continuity
 Neighborhood bases, first and second countable, sequences and closures
 Uniform convergence (Section 21)
 Quotient topology (sketched) and connectedness (Sections 22 and 23)
 More connectedness (Section 23 continued)
 Connected subsets of the reals (Section 24)
 Components and locally connected (sketched) then compactness (Section 25 and 26)
 More compactness (Section 26)
 Compactness in the reals (Section 27)
 Extreme value theorem more results (Section 27)
 Limit point and other types of compactness (Section 28)
 Review for exam
 "In the midst"-term Exam #2
 Extra time on the Exam and Nets (Supplemental section on nets)
 More on nets and introduction to filters (See links to handout)
 Ultrafilters and convergence (handout)
 Tychonoff's theorem (handout) & a bit about separation axioms (Sections 30-33)
 Separation axioms and odds & ends (see handout)
 compactifications: 1 point and Stone-Cech (Sections 29 and 38)
 a touch of manifold theory




Tentative Class Topics for Class #...

 Set theory basics, functions, relations (Sections 1-3)
 More basics
 Constructing the real numbers and infinite cartesian products (Sections 4-5)
 Finite, countable, and uncountable (Sections 6-7)
 Axiom of Choice, well orderings, etc. (Sections 8-11)
 Catch up & Review
 Set Test
 Topological Spaces (Section 12)
 Bases and subbases (Section 13)
 Order and product topologies (Sections 14-15)
 Subspaces, closed sets, & limit points (Sections 16-17)
 Continuous functions (Section 18)
 More on continuity
 Box and product topologies (Section 19)
 Metric spaces (Section 20) 
 More on metric spaces (Section 21)
 Finishing metric spaces 
 Quotient spaces (Section 22)
 Connectedness (Section 23)
 Connected subspaces of the reals (Section 24)
 Connected components (Section 25)
 Compactness (Section 26)
 Compactness continued
 Compact subspaces of the reals (Section 27)
 Limit point compactness (Section 28)
 Local compactness (Section 29)
 Catch up & Review
 "Midterm" Exam
 Filters [Wilansky supplement]
 Nets [Wilansky supplement]
 The Tychonoff Theorem (Section 37)
 Countability Axioms (Section 30)
 Separation Axioms (Section 31)
 Normal (Section 32)
 Urysohn's Lemma (Section 33)
 Urysohn's metrization theorem (Section 34)
 Tieze's extension theorem (Section 35)
 A bit about manifolds? (Section 36)
 Compactifications? (Section 38)
 Stone-Cech? 
 Other bits of analysis & function spaces?
 Stone-Weierstrass? Some homotopy theory?
 Catch up & Review
 Final Exam





Last Updated December 11th, 2014.