definition of locally topologically Euclidean topological space
Topics
About: topological space
The table of contents of this article
Starting Context
- The reader knows a definition of topological space.
- The reader knows a definition of neighborhood of point on topological space.
- The reader knows a definition of homeomorphism.
- The reader knows a definition of Euclidean topological space.
Target Context
- The reader will have a definition of locally topologically Euclidean topological space.
Orientation
There is a list of definitions discussed so far in this site.
There is a list of propositions discussed so far in this site.
Main Body
1: Structured Description
Here is the rules of Structured Description.
Entities:
\( \mathbb{R}^d\): \(= \text{ the Euclidean topological space }\)
\(*T\): \(\in \{\text{ the topological spaces }\}\)
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Conditions:
\(\forall t \in T (\exists U_t \in \{\text{ the open neighborhoods of } t \text{ on } T\}, \exists U_r \in \{\text{ the open neighborhoods of } r \text{ on } \mathbb{R}^d\} (\exists f: U_t \to U_r \in \{\text{ the homeomorphisms }\}))\)
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2: Note
The expression, "topologically Euclidean topological space", may seem redundant, but is not so strictly speaking, because 'Riemannianly Euclidean topological space' is possible because any Riemannian manifold is a topological space, as well as 'only topologically Euclidean Riemannian manifold' is of course possible.
