Proof That a Finite Subset of a Hausdorff Space is Closed Print TheoremIfis a Haudorff space and ifis a finite subset ofthenis closed.ProofLetandA neighbourhoodofexists such thatHenceandis open andis closed.By induction, any finite subsetis closed. Prev Next Add comment Name (required) E-mail (required, but will not display) Refresh SendCancel