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Continuous Functions on Sequentially Compact Set

TOPO-E2QYT2

Which of the following statements is (are) true regarding continuous real-valued functions on a sequentially compact set?

Select ALL that apply.

A

A continuous function on a sequentially compact set must have maximum.

B

A continuous function on a sequentially compact set must have minimum.

C

For any $a\in\mathbb{R}$, any continuous function $f$ on a sequentially compact set, $f^{-1}(a)$ is also sequentially compact.

D

The set of continuous functions on a sequentially compact set has cardinality no greater than the cardinality of $\mathbb{R}$.