definition of simply connected 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 path-connected topological space.
- The reader knows a definition of fundamental group of topological space at point.
Target Context
- The reader will have a definition of simply connected 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:
\(*T\): \(\in \{\text{ the path-connected topological spaces }\}\)
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Conditions:
\(\forall p \in T (\pi_1 (T, p) = \{1\})\) where \(\pi_1 (T, p)\) is the fundamental group.
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2: Natural Language Description
Any path-connected topological space, \(T\), such that at each point, \(p \in T\), the fundamental group is \(\pi_1 (T, p) = \{1\}\)
