definition of boundary of subset of topological space
Topics
About: topological space
The table of contents of this article
Starting Context
- The reader knows a definition of closure of subset of topological space.
Target Context
- The reader will have a definition of boundary of subset of 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:
\( T\): \(\in \{\text{ the topological spaces }\}\)
\( S\): \(\subseteq T\)
\(*\dot{S}\): \(= \overline{S} \cap \overline{T \setminus S}\), \(\subseteq T\)
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Conditions:
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Or we may denote \(\dot{S}\) as \(Bou (S)\), because when the \(S\) part is long like \((\cup_{j \in J} S_j) \cap S\), the upper dot may not be clear what it qualifies.
