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 26 pages are in this category, out of 26 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
E
L
- Local Connectedness is not Preserved under Continuous Mapping
- Local Connectedness is not Preserved under Infinite Product
- Locally Connected Separable Topological Space has Countably Many Components
- Locally Connected Space is not necessarily Connected
- Locally Connected Space is not necessarily Locally Path-Connected
- Locally Path-Connected Space is Locally Connected