# Category:Irreducible Spaces

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This category contains results about Irreducible Spaces.

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

A topological space $T = \struct {S, \tau}$ is **irreducible** if and only if every two non-empty open sets of $T$ have non-empty intersection:

- $\forall U, V \in \tau: U, V \ne \O \implies U \cap V \ne \O$

## Subcategories

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

### C

### P

### T

## Pages in category "Irreducible Spaces"

The following 30 pages are in this category, out of 30 total.

### C

### E

### I

- Indiscrete Space is Irreducible
- Irreducible Component is Closed
- Irreducible Components of Hausdorff Space are Points
- Irreducible Hausdorff Space is Singleton
- Irreducible Space is Connected
- Irreducible Space is Locally Connected
- Irreducible Space is not necessarily Path-Connected
- Irreducible Space is Pseudocompact
- Irreducible Space with Finitely Many Open Sets is Path-Connected
- Irreducible Subspace is Contained in Irreducible Component