We give the standard examples (i) Comb space and (ii) Topologists' sine-curve. The approach to Comb space here may be easier for some of you who have already watched path-connectedness -3.
Timestamp provided by Ishwarya.
0:00 Introduction
0:46 Brief description about this Lecture
2:43 Example 1: Combspace
7:46 Defining X
8:37 Observation 1: X is connected
10:06 Claim: X is not path connected
13:47 Idea to complete the proof
28:53 Break
29:47 About Topologist sine curve
30:11 Graph of the curve
30:56 Example 2: Topologist sine curve
34:48 X= S U {(0,0)} is not path connected
41:09 Important trick