831: Subbasis of Topological Space

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definition of subbasis 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: Note

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Starting Context

• The reader knows a definition of basis of topological space.

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Target Context

• The reader will have a definition of subbasis 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:
$T$: $\in \{\text{ the topological spaces }\}$
$\ast S$: $\subseteq Pow(T)$
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Conditions:
$B:=\text{ the set of the intersections of each finite subset of }S\in \{\text{ the bases of }T\}$
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2: Note

When the topology of $T$ is not determined yet, any $S$ that contains $T$ and $\mathrm{\varnothing }$ generates a topology, by the proposition that for any set, any set of subsets with the whole set and the empty set constitutes a subbasis.

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References

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