44: Topological Path

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definition of topological path

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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 topological space.
• The reader knows a definition of Euclidean topological space.
• The reader knows a definition of subspace topology.
• The reader knows a definition of continuous map.

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Target Context

• The reader will have a definition of topological path.

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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:
$T$: $\in \{\text{ the topological spaces }\}$
$[a,b]$: $\in \{\text{ the closed intervals of }\mathbb{R}\}$ as the subspace of the Euclidean topological space, $\mathbb{R}$
$\ast \lambda$: $:[a,b]\to T$
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Conditions:
$\lambda \in \{\text{ the continuous maps }\}$.
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2: Natural Language Description

For any topological space, $T$, and any closed $\mathbb{R}$ interval as the subspace of the Euclidean topological space, $\mathbb{R}$, $[a,b]$, any continuous map, $\lambda :[a,b]\to T$

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References

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