Indiscrete Space is T4

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Theorem

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


Then $T$ is a $T_4$ space.


Proof

We have that an indiscrete space is a $T_5$ space.

Then we have that a $T_5$ Space is a $T_4$ Space.

$\blacksquare$


Sources