countably compact
A topological space
is said to be countably compact if every countable
open cover has a finite subcover.
Countable compactness is equivalent to limit point compactness if is spaces, and is equivalent to compactness (http://planetmath.org/Compact
) if is a metric space.
| Title | countably compact |
|---|---|
| Canonical name | CountablyCompact |
| Date of creation | 2013-03-22 12:06:43 |
| Last modified on | 2013-03-22 12:06:43 |
| Owner | Evandar (27) |
| Last modified by | Evandar (27) |
| Numerical id | 8 |
| Author | Evandar (27) |
| Entry type | Definition |
| Classification | msc 54D20 |
| Synonym | countable compactness |
| Related topic | Compact |
| Related topic | Lindelof |
| Related topic | LimitPointCompact |