Question

Prove that every closed subspace of a locally compact space is locally compact​

Answer 1

ANSWER:-

In particular, closed neighborhoods form a neighborhood basis of every point (since compact in Hausdorff is closed). Therefore, a locally compact Hausdorff space is always regular. ... Then a subspace A Ç X is locally compact if and only if it is of the form A = U n F for some U Ç X open and F Ç X closed. Proof.

BY - VAIBHAV TYAGI