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Indiscrete Topology#

Theorem: Indiscrete Topology

Let \(X\) be a set.

The collection \(\{\varnothing, X\}\) which contains only the empty set \(\varnothing\) and \(X\) itself is a topology on \(X\).

Definition: Indiscrete Topology

We call \(\{\varnothing, X\}\) the indiscrete topology or trivial topology on \(X\).

Proof

TODO