Sequential Compactness

Definition

Consider a Topological Space $(X,\mathcal{T})$. The set $X$ is sequentially compact if every subsequence of points of $X$ has a converged subsequence.

Facts

Consider a metrizable space $(X,\mathcal{T})$. Then, $X$ is compact if and only if $X$ is Limit Point Compact if and only if $X$ is Sequentially Compact

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