Definition:Relatively Compact Subspace

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Definition

Let $T = \left({S, \tau}\right)$ be a topological space.

Let $T_H = \left({H, \tau_H}\right)$ be a subspace of $T$.

Let $\operatorname{cl} \left({H}\right)$ be the closure of $H$ in $T$.


Then $T_H$ is relatively compact in $T$ if and only if $\operatorname{cl} \left({H}\right)$ is compact.


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