definition of topological path-connected component
Topics
About: topological space
The table of contents of this article
Starting Context
- The reader knows a definition of topological path-connected-ness of 2 points.
- The reader admits the proposition that topological path-connected-ness of 2 points is an equivalence relation.
Target Context
- The reader will have a definition of topological path-connected component.
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:
\( T\): \(\in \{\text{ the topological spaces }\}\)
\( R\): \(= \text{ the topological path-connected-ness of } 2 \text{ points on } T\)
\( T / R\): \(= \text{ the set of the equivalence classes }\)
\(*C\): \(\in T / R\)
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Conditions:
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2: Note
As \(R\) is an equivalence relation, by the proposition that topological path-connected-ness of 2 points is an equivalence relation, the definition is valid.
