definition of locally compact topological space
Topics
About: topological space
The table of contents of this article
- Starting Context
- Target Context
- Orientation
- Main Body
- 1: Structured Description
- 2: Natural Language Description
Starting Context
- The reader knows a definition of neighborhood of point.
- The reader knows a definition of compact subset of topological space.
Target Context
- The reader will have a definition of locally compact 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:
\(*T\): \(\in \{\text{ the topological spaces }\}\)
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Conditions:
\(\forall p \in T, \forall N_p \subseteq T \in \{\text{ the neighborhoods of } p\} (\exists C_p \subseteq T \in \{\text{ the compact neighborhoods of } p\} (C_p \subseteq N_p))\)
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2: Natural Language Description
Any topological space, \(T\), such that for each point, \(p \in T\), and each neighborhood, \(N_p \subseteq T\), of \(p\), there is a compact neighborhood, \(C_p \subseteq T\), of \(p\) such that \(C_p \subseteq N_p\)
