definition of finite-product metric space
Topics
About: metric space
The table of contents of this article
Starting Context
- The reader knows a definition of finite-product metric.
- The reader knows a definition of metric space.
Target Context
- The reader will have a definition of finite-product metric 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:
\( J\): \(\in \{\text{ the finite index sets }\}\)
\( \{M_j \vert j \in J\}\): \(M_j \in \{\text{ the metric spaces }\}\) with any metric, \(dist_j\)
\( \times_{j \in J} M_j\): \(= \text{ the product set }\)
\( dist\): \(= \text{ the finite-product metric for } \times_{j \in J} M_j\)
\(*(\times_{j \in J} M_j, dist)\)
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Conditions:
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