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| Title of object: |
locally connected |
| Canonical Name: |
LocallyConnected |
| Type: |
Definition |
| Created on: |
2002-05-17 22:31:32 |
| Modified on: |
2002-05-17 22:31:32 |
| Classification: |
msc:54D05 |
| Defines: |
locally path connected |
Revision comment (for changes between this and next version):
| Changes for correction #2554 ('linking issues'). |
Preamble:
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Content:
A topological space $X$ is {\em locally connected} at a point $x \in X$ if every neighborhood $U$ of $x$ contains a connected neighborhood $V$ of $x$. The space $X$ is {\em locally connected} if it is locally connected at every point $x \in X$.
A topological space $X$ is {\em locally path connected} at a point $x \in X$ if every neighborhood $U$ of $x$ contains a path connected neighborhood $V$ of $x$. The space $X$ is {\em locally path connected} if it is locally path connected at every point $x \in X$. |
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