Open Sets in Indiscrete Topology

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Theorem

Let $T = \left({S, \left\{{\varnothing, S}\right\}}\right)$ be an indiscrete topological space.

Let $H \subseteq S$.


$H$ is an open set of $T$ if and only if either $H = S$ or $H = \varnothing$.


Proof

A set $U$ is open in a topology $\tau$ if $U \in \tau$.

In $\tau = \left\{{\varnothing, S}\right\}$, the only open sets are $\varnothing$ and $S$.

$\blacksquare$


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