Indiscrete Space is Connected
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Theorem
Let $T = \struct {S, \set {\O, S} }$ be an indiscrete topological space.
Then $T$ is connected.
Proof
We have that an Indiscrete Space is Path-Connected.
Then we have that a Path-Connected Space is Connected.
$\blacksquare$
Sources
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text {II}$: Counterexamples: $4$. Indiscrete Topology: $9$