Prove that a topological space (X, ?) is connected if and only if for every pair of distinct poi

Name: Prove that a topological space (X, ?) is connected if and only if for every pair of distinct points x and y in X, there is a connected set C such that x, y ? C and C ? X.
Uploaded: 2023-01-19T12:07:06-08:00
Duration: 4 min 9 s
Channel: Madhur L
Description: Prove that a topological space (X, ?) is connected if and only if for every pair of distinct points x and y in X, there is a connected set C such that x, y ? C and C ? X.

Question

Madhur L · Accepted Answer

Let € be a point in X and y a point in 9. We want to find a connected set C that includes € and

Question

Prove that a topological space (X, ?) is connected if and only if for every pair of distinct points x and y in X, there is a connected set C such that {x, y} ? C and C ? X.

Please give Ace some feedback