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.