Subset of Indiscrete Space is Compact and Sequentially Compact
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Theorem
Let $T = \struct {S, \set {\O, S} }$ be an indiscrete topological space.
Let $H \subseteq S$.
Subset of Indiscrete Space is Compact
$H$ is compact in $T$.
Subset of Indiscrete Space is Sequentially Compact
$H$ is sequentially compact in $T$.
Sources
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text {II}$: Counterexamples: $4$. Indiscrete Topology: $3$