Category:Locally Euclidean Spaces
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This category contains results about Locally Euclidean Spaces.
Let $M$ be a topological space.
Let $d \in \N$ be a natural number.
Then $M$ is a locally Euclidean space of dimension $d$ if and only if each point in $M$ has an open neighbourhood which is homeomorphic to an open subset of Euclidean space $\R^d$.
Subcategories
This category has only the following subcategory.
Pages in category "Locally Euclidean Spaces"
The following 6 pages are in this category, out of 6 total.
L
- Locally Euclidean Space has Countable Local Basis Homeomorphic to Open Balls
- Locally Euclidean Space has Countable Neighborhood Basis Homeomorphic to Closed Balls
- Locally Euclidean Space is First-Countable
- Locally Euclidean Space is Locally Compact
- Locally Euclidean Space is Locally Connected
- Locally Euclidean Space is Locally Path-Connected