# Category:Locally Connected Spaces

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This category contains results about **Locally Connected Spaces**.

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

A topological space $T = \struct{S, \tau}$ is **locally connected** if and only if each point of $T$ has a local basis consisting entirely of connected sets in $T$.

## Subcategories

This category has the following 5 subcategories, out of 5 total.

## Pages in category "Locally Connected Spaces"

The following 23 pages are in this category, out of 23 total.

### C

- Cantor Space is not Locally Connected
- Compact Complement Topology is Locally Connected
- Component of Locally Connected Space is Open
- Connected Space is not necessarily Locally Connected
- Continuous Mapping from Compact Space to Hausdorff Space Preserves Local Connectedness
- Countable Complement Space is Locally Connected