definition of topological quasi-connected component
Topics
About: topological space
The table of contents of this article
Starting Context
- The reader knows a definition of topological quasi-connectedness of 2 points.
- The reader knows a definition of set of equivalence classes of set by equivalence relation.
Target Context
- The reader will have a definition of topological quasi-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:
\( T\): \(\in \{\text{ the topological spaces }\}\)
\( R\): \(= \text{ the quasi-connectedness of } 2 \text{ points on } T\)
\( T / R\): \(= \text{ the set of the equivalence classes of } T \text{ by } R\)
\(*C\): \(\in T / R\)
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Conditions:
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2: Note
This is called "quasi-connected component", because each connected component of \(T\) is contained in a quasi-connected component of \(T\), but not necessarily vice versa, by the proposition that for any topological space, each connected component is contained in the corresponding quasi-connected component.
