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Topology

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Properties of Relatively Compact Subspaces

TOPO-N0UILK

Which of the following statements about relatively compact subsets is(are) true?

A

If $A\subset B$ are two subsets, $B$ is relatively compact, then $A$ is relatively compact.

B

If $X$ is Hausdorff, $A\subset B$ are two subsets, $B$ is relatively compact, then $A$ is relatively compact.

C

The intersection of two relatively compact subsets is relatively compact.

D

The union of two relatively compact subsets is relatively compact.

E

There are topological spaces that are not homeomorphic to any relatively compact subspace.