definition of boundary of subset of topological space
Topics
About: topological space
The table of contents of this article
- Starting Context
- Target Context
- Orientation
- Main Body
- 1: Structured Description
- 2: Natural Language Description
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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2: Natural Language Description
For any topological space, \(T\), and any subset, \(S \subseteq T\), the subset, \(\dot{S} = \overline{S} \cap \overline{T \setminus S} \subseteq T\)
