definition of product topological space
Topics
About: topological space
The table of contents of this article
- Starting Context
- Target Context
- Orientation
- Main Body
- 1: Structured Description 1
- 2: Natural Language Description 1
- 3: Structured Description 2
- 4: Natural Language Description 2
Starting Context
- The reader knows a definition of topological space.
- The reader knows a definition of product set.
- The reader knows a definition of product topology.
Target Context
- The reader will have a definition of product 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 1
Here is the rules of Structured Description.
Entities:
\( A\): \(\in \{\text{ the possibly uncountable infinite index sets }\}\)
\( \{T_\alpha \vert \alpha \in A\}\): \(T_\alpha \in \{\text{ the topological spaces }\}\)
\(*T\): \(= \times_{\alpha \in A} T_\alpha\) with the product topology
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Conditions:
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2: Natural Language Description 1
For any possibly uncountable infinite index set, \(A\), and any topological spaces, \(\{T_\alpha \vert \alpha \in A\}\), the product set, \(T := \times_{\alpha \in A} T_\alpha\), with the product topology
3: Structured Description 2
Here is the rules of Structured Description.
Entities:
\( \{T_1, ..., T_n\}\): \(T_j \in \{\text{ the topological spaces }\}\)
\(*T\): \(= T_1 \times ... \times T_n\) with the product topology
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Conditions:
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4: Natural Language Description 2
For any topological spaces, \(\{T_1, ..., T_n\}\), the product set, \(T := T_1 \times ... \times T_n\), with the product topology
