# Category:Paracompact Spaces

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This category contains results about **Paracompact Spaces**.

Let $T = \struct {S, \tau}$ be a topological space.

$T$ is **paracompact** if and only if every open cover of $S$ has an open refinement which is locally finite.

## Subcategories

This category has the following 3 subcategories, out of 3 total.

## Pages in category "Paracompact Spaces"

The following 33 pages are in this category, out of 33 total.

### E

### L

- User:Leigh.Samphier/Topology/Characterization of Paracompact Space by Precise Refinement
- User:Leigh.Samphier/Topology/Characterization of Paracompactness in T3 Space
- User:Leigh.Samphier/Topology/Characterization of Paracompactness in T4 Space
- User:Leigh.Samphier/Topology/Paracompact T2 Space is Normal
- User:Leigh.Samphier/Topology/Paracompact T2 Space is Regular
- User:Leigh.Samphier/Topology/Paracompact T2 Space is T3 Space
- User:Leigh.Samphier/Topology/Paracompact T2 Space is T4 Space
- User:Leigh.Samphier/Topology/T3 Space is Fully T4 iff Paracompact
- User:Leigh.Samphier/Topology/T3 Space with Sigma-Locally Finite Basis is Paracompact
- Lindelöf T3 Space is Paracompact

### P

- Paracompact Countably Compact Space is Compact
- Paracompact Space is Countably Paracompact
- Paracompact Space is Metacompact
- Paracompactness is not always Preserved under Open Continuous Mapping
- Paracompactness is Preserved under Projections
- Product of Countable Discrete Space with Sierpiński Space is Paracompact
- Product of Paracompact Spaces is not always Paracompact