definition of lower semicontinuous map from topological space into \(1\)-dimensional extended Euclidean topological space
Topics
About: topological space
The table of contents of this article
Starting Context
Target Context
- The reader will have a definition of lower semicontinuous map from topological space into \(1\)-dimensional extended Euclidean 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:
\( T_1\): \(\in \{\text{ the topological spaces }\}\)
\( \overline{\mathbb{R}}\): \(= \text{ the extended Euclidean topological space }\)
\(*f\): \(: T_1 \to \overline{\mathbb{R}}\)
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Conditions:
\(\forall t_1 \in T_1 (f \in \{\text{ the maps lower semicontinuous at } t_1\})\)
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