mod08lec49 - Compactness and Sequential Compactness in arbitrary topological spaces
We show that for general topological spaces, compactness and sequential compactness are independent notions, i.e. neither implies the other. We give counterexamples for both-- a space which is compact but not sequentially compact, and a space which is sequentially compact but not compact. These counterexamples give us an idea how and why the equivelence of these concepts in the case of metric spaces, breaks down for general spaces.
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