Proof That a Finite Subset of a Topological Space is Sequentially Compact
A finite subsetof a topological spaceis sequentially compact.
A subsetof a topological spaceis sequentially compact if every sequence in contains a subsequence which converges to a point in
Letbe a finite subset ofand letbe a sequence in
Sinceis finite, at lease one of the elements insay x_0 , occurs an infinite number of times, We can choose a subsequence consisting of the termswhich converges to