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Last-modified: 2010-12-04 (土) 14:57:06

Definition Edit

A topological space is said to be hemicompact if there is a sequence of compact subsets (called admissible sequence) such that every compact subset is contained in some member of the sequence.

Property Edit

  • A hemicompact space is the union of the admissible sequence since every singleton in the space is a compact set.
  • Every first countable hemicompact space is locally compact.
  • If X is hemicompact, then the space C(X) of all continuous functions from X to the real is metrizable. The metric is given by
    where K_n are the admissible sequence.

Reference Edit

Willard, Stephen, General Topology, Dover (2004).