Compactness (mathematics) | Properties of topological spaces

Hemicompact space

In mathematics, in the field of topology, a topological space is said to be hemicompact if it has a sequence of compact subsets such that every compact subset of the space lies inside some compact set in the sequence. Clearly, this forces the union of the sequence to be the whole space, because every point is compact and hence must lie in one of the compact sets. (Wikipedia).

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Related pages

Pseudometric space | Compact space | Topological space | Metric space | Mathematics | Lindelöf space | Topology | Σ-compact space | Locally compact space | Compact-open topology | First-countable space