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Hausdorff defines compactness by requiring that every infinite subset S of a set E has a limit point that lies within E itself. This prevents infinite subsets from escaping to infinity without accumulating inside the set.

Conditions: E is a set.; S is an arbitrary infinite subset of E (S ⊂ E).; The limit point must belong to E.

Hausdorff defines compactness by requiring that every infinite subset S of a set E has a limit point that lies within E itself. This prevents infinite subsets from escaping to infinity without accumulating inside the set.

Conditions: E is a set.; S is an arbitrary infinite subset of E (S ⊂ E).; The limit point must belong to E.