673: Locally Finite Set of Subsets of Topological Space

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definition of locally finite set of subsets of 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 power set of set.
• The reader knows a definition of neighborhood of point.

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Target Context

• The reader will have a definition of locally finite set of subsets of 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:
$T$: $\in \{\text{ the topological spaces }\}$
$\ast S$: $\in Pow(T)$
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Conditions:
$\mathrm{\forall }p\in T(\mathrm{\exists }{N}_p\subseteq T\in \{\text{ the neighborhoods of }p\}(\{S^{\prime }\in S|S^{\prime }\cap N_p\ne \mathrm{\varnothing }\}\in \{\text{ the finite sets }\}))$
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2: Natural Language Description

For any topological space, $T$, any set of subsets, $S\in Pow(T)$, such that for each $p\in T$, there is a neighborhood, $N_p\subseteq T$, of $p$, such that only finite number of elements of $S$ intersects $N_p$

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References

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