518: Simply Connected Topological Space

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definition of simply connected topological space

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Topics

About: topological space

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The table of contents of this article

• Starting Context
• Target Context
• Orientation
• Main Body
• 1: Structured Description
• 2: Natural Language Description

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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.

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Target Context

• The reader will have a definition of simply connected topological space.

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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.

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Main Body

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1: Structured Description

Here is the rules of Structured Description.

Entities:
$\ast T$: $\in \{\text{ the path-connected topological spaces }\}$
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Conditions:
$\mathrm{\forall }p\in T({\pi }_1(T,p)=\{1\})$ 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 ${\pi }_1(T,p)=\{1\}$

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References

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