558: Boundary of Subset of Topological Space

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definition of boundary of subset 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 closure of subset of topological space.

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Target Context

• The reader will have a definition of boundary of subset 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:
$T$: $\in \{\text{ the topological spaces }\}$
$S$: $\subseteq T$
$\ast \dot{S}$: $=\bar{S}\cap \overline{T\setminus S}$, $\subseteq T$
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Conditions:
//

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2: Natural Language Description

For any topological space, $T$, and any subset, $S\subseteq T$, the subset, $\dot{S}=\bar{S}\cap \overline{T\setminus S}\subseteq T$

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References

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