definition of topological path
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 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.
Target Context
- The reader will have a definition of topological path.
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:
\( T\): \(\in \{\text{ the topological spaces }\}\)
\( [a, b]\): \(\in \{\text{ the closed intervals of } \mathbb{R}\}\) as the subspace of the Euclidean topological space, \(\mathbb{R}\)
\(*\lambda\): \(: [a, b] \to T\)
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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, \(\lambda: [a, b] \to T\)
