|
Lecture
1
(August 06, 2004)
|
Sets and Maps |
|
Lecture
2 (August
09, 2004)
|
Injective, Surjective,
Bijective Maps |
|
Lecture
3 (August
11, 2004)
|
Finite
sets, Cardinal numbers |
|
Lecture
4 (August
13, 2004)
|
Mathematical Induction
---
Well-ordering principle for natural
numbers |
|
Lecture
5 (August
16, 2004) |
Ordered sets |
|
Lecture
6 (August
18, 2004)
|
Transfinite
induction |
|
Lecture 7
(August
20, 2004)
|
Infinite sets ---
Countable and uncountable sets |
|
Lecture 8
(August
23, 2004)
|
Metric Spaces |
|
Lecture 9
(August
25, 2003)
|
Continuous
maps between Metric Spaces |
|
Lecture 10
(August
27, 2003)
|
Topological Spaces |
|
Lecture 11
(August
30, 2003) |
Closure, Interior and Boundary in
Topological Spaces
|
|
Lecture 12
(September
01, 2003) |
Base for a Topology,
Definitions of Second Countable, Separable and Lindelof spaces |
|
Lecture 13
(September
03, 2003) |
Neighbourhood base for a Topology
|
|
Lecture 14
(September
06, 2003) |
Schoerder Berstein
Theorem
|
|
Lecture 15
(September
08, 2003) |
Countablity Axioms ---
Properties of
First countable, Second
countable, Lindeloef and separable spaces
|
|
Lecture 16
(September
10, 2003) |
Examples ---
Sorgenfrey line, Slotted
plane |
|
Lecture 17
(September
13, 2003) |
Continuous
maps, ---
Homeomorphisms |
|
Lecture 18
(September
15, 2004) |
Properties of Continuous maps ---
Upper and Lower semicontinuity, Algebra of
Continuous functions |
|
Lecture 19
(September
17, 2004) |
Group of Homeomorphisms, Topological
Properties |
|
Lecture 20
(September
20, 2004) |
Product Spaces |
|
Lecture 21
(September
22, 2004) |
Product Spaces
-- Contd |
|
Lecture 22
(September
24, 2004) |
Quotient Spaces |
|
Lecture 23
(September
27, 2004) |
Quotient Spaces
-- Examples |
|
Lecture 24
(September
29, 2003) |
Missed |
|
Lecture 25
(October
01, 2004) |
Missed |
|
Lecture 26
(October
04, 2004) |
Missed |
|
Lecture 27
(October
06, 2004) |
Convergence in topological spaces
--- Inadequacy of sequences, Examples |
|
Lecture 28
(October
08, 2004) |
Nets --- Examples |
|
Lecture 29
(October
11, 2004) |
Characterizations of closure and
continuity using nets
--- Examples |
|
Lecture 30
(October
13, 2004) |
Filters --- Examples |
|
Lecture 31
(October
15, 2004) |
Compact Spaces ---
Characterization, Tychonoff
theorem |
|
Lecture 32
(October
18, 2004) |
Variations of compactness ---
Sequentially, Countably Compactness,
Examples |
|
Lecture 33
(October
20, 2004) |
Compactness and Countability |
|
Lecture 34
(October
22, 2004) |
|
|
Lecture 35
(October
25, 2004) |
One point compactification --- Examples |
|
Lecture 36
(October
27, 2004) |
Projective Spaces
Holiday |
|
Lecture 37
(October
29, 2004) |
Postponed to Monday November 01 |
|
Lecture 38
(November
01, 2004) |
Connected Spaces
Holiday
|
|
Lecture 39
(November
03, 2004) |
Path-Connected Spaces |
|
Lecture 40
(November
05, 2004) |
Compactness in normed linear spaces |
|
Lecture 41
(November
08, 2004) |
Complete metric spaces ---
Completion, Baire's theorem. |
|
Lecture 42
(November
10, 2004) |
Topology of Uniform convergence |
|
Lecture 43
(November
11,, 2004) |
Stone-Weierstrass theorems ---
Examples
Proponed from November 12 (Holiday) |
|
Lecture 44
(November
16, 2004) |
Function spaces --- Arzela- Ascoli
theorems
Postponed from November 15 (Holiday) |
|
Lecture 45
(November
17, 2004) |
Separation axioms ---
Tiezte Extension theorem |
|
Lecture 46
(November
19, 2004) |
Urysohn's lemma |
|
Lecture 47
(November
22, 2004) |
|
|
Lecture 48
(November
24, 2004) |
|
|
Lecture 49
(November
26, 2004) |
Holiday |
|
Lecture 50
(November
29, 2004) |
|
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