Generating Topologies -3

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This is the third of the series of four lectures on a unified view of various constructions such as subspace, product and quotient topologies. We now look at a question which is in some sense dual to the question of Lecture 1 and discuss with the quotient topology. We also look at two simple and confidence-building examples of quotient topology.

Time-stamp provided by Ishwarya.
0:00 Introduction
0:47 Brief description about this Lecture
2:07 Discussion about Case 2 in Generating Topologies-1
4:34 t:= { V in Y / inverse image of V is open in X} is a topology
11:56 Claim 1: f is continuous
12:42 Claim 2: t is the largest topology on Y which makes f is continuous
15:12 Summary
17:05 Concrete Case: Equivalence Relation
22:01 Two natural ways of producing an Equivalence relation
26:13 Equivalence Relation on R2 with Standard Topology
30:29 Equivalence class of (a,b) in R2.
33:25 Example- unit circle
35:40 Example- open ball
37:46 Set V consists of all vertical lines Lc, c non-negative is not open in R2/~.
43:08 Equivalence relation on Z with discrete topology
46:41 Quotient Topology on Z/~