672: Locally Compact Topological Space

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definition of locally compact topological space

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Topics

About: topological space

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The table of contents of this article

• Starting Context
• Target Context
• Orientation
• Main Body
• 1: Structured Description
• 2: Natural Language Description

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Starting Context

• The reader knows a definition of neighborhood of point.
• The reader knows a definition of compact subset of topological space.

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Target Context

• The reader will have a definition of locally compact topological space.

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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.

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Main Body

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1: Structured Description

Here is the rules of Structured Description.

Entities:
$\ast T$: $\in \{\text{ the topological spaces }\}$
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Conditions:
$\mathrm{\forall }p\in T,\mathrm{\forall }{N}_p\subseteq T\in \{\text{ the neighborhoods of }p\}(\mathrm{\exists }{C}_p\subseteq T\in \{\text{ the compact neighborhoods of }p\}(C_p\subseteq N_p))$
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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 $C_p\subseteq N_p$

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References

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