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Show that if $X$ is compact, and if $A$ is a closed subset of $X,$ then $A$ is also compact.

Show that if $X$ is compact, and if $A$ is a closed subset of $X,$ then $A$(with the subspace topology ) is also compact. A HINT: Use the subspace topology to relate open sets in $A$ with open sets in $X;$ somehow you need to find an open cover of $X.$ Still I am unable […]