In mathematics, in the field of topology, a Hausdorff 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.
[1] 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.
Every hemicompact space is σ-compact[2] and if in addition it is first countable then it is locally compact.
If a hemicompact space is weakly locally compact, then it is exhaustible by compact sets.
with the compact-open topology is metrizable.
lies inside some compact set in this sequence (the existence of such a sequence follows from the hemicompactness of
which induces the compact-open topology.
This topology-related article is a stub.