Last-modified: 2010-12-02 (木) 22:22:53
A topological space is called finally compact if any open cover of this space contains a countable subcover.
- 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.
- 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.
A.V. Arhangel'skii (ed), General topology III: paracompactness, function spaces, descriptive theory, Springer (1989)