definition of regular topological space
Topics
About: topological space
The table of contents of this article
Starting Context
- The reader knows a definition of topological space.
- The reader knows a definition of closed subset of topological space.
- The reader knows a definition of neighborhood of point on topological space.
- The reader knows a definition of neighborhood of subset of topological space.
Target Context
- The reader will have a definition of regular 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:
\(*T\): \(\in \{\text{ the topological spaces }\}\)
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Conditions:
\(\forall t \in T (\{t\} \in \{\text{ the closed subsets of } T\})\)
\(\land\)
\(\forall t \in T, \forall C \in \{\text{ the closed subsets of } T\} \text{ such that } t \notin C (\exists U_t \in \{\text{ the open neighborhoods of } t\}, \exists U_C \in \{\text{ the open neighborhoods of } C\} (U_t \cap U_C = \emptyset))\)
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