# Category:Countably Compact Spaces

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This category contains results about **Countably Compact Spaces**.

Definitions specific to this category can be found in Definitions/Countably Compact Spaces.

A topological space $T = \struct {S, \tau}$ is **countably compact** if and only if:

- every countable open cover of $T$ has a finite subcover.

## Subcategories

This category has the following 2 subcategories, out of 2 total.

## Pages in category "Countably Compact Spaces"

The following 34 pages are in this category, out of 34 total.

### C

- Compact Space is Countably Compact
- Countable Compactness is Preserved under Continuous Surjection
- Countable Complement Space is not Countably Compact
- Countably Compact First-Countable Space is Sequentially Compact
- Countably Compact Lindelöf Space is Compact
- Countably Compact Metric Space is Compact
- Countably Compact Metric Space is Sequentially Compact
- Countably Compact Space is Countably Paracompact
- Countably Compact Space is Pseudocompact
- Countably Compact Space is Weakly Countably Compact
- Countably Compact Space satisfies Countable Finite Intersection Axiom
- Countably Infinite Set in Countably Compact Space has Omega-Accumulation Point