Proof That a Continuous Image of a Sequentially Compact Set is Sequentially Compact
A continuous image of a sequentially compact set is sequentially compact.
Letbe a continuous function and letbe a sequentially compact subset of
Letbe a sequence inthen there exists a sequence insuch that
Since A is sequentially compactcontains a subsequencewhich converges to a point
Thenconverges tohenceis sequentially compact.