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finally compact

Last-modified: 2010-12-02 (木) 22:22:53

Definition Edit

A topological space is called finally compact if any open cover of this space contains a countable subcover.

Property Edit

  • Every Lindeloef space is strongly paracompact.
  • Every separable metacompact space is finally compact.
  • For separable T_3-spaces, metacompactness, paracompactness, strong paracompactness and final compactness are equivalent.
  • A connected T_3-space is strongly paracompact if and only if it is finally compact.

Remark Edit

  • This space is usually called Lindeloef but sometimes finally compact regular space is called a Lindeloef space. The term "Lindeloef" above stands for finally compact regular spaces.

Reference Edit

A.V. Arhangel'skii (ed), General topology III: paracompactness, function spaces, descriptive theory, Springer (1989)