definition of support of map from topological space into ring or module
Topics
About: topological space
The table of contents of this article
Starting Context
- The reader knows a definition of topological space.
- The reader knows a definition of ring.
- The reader knows a definition of %ring name% module.
- The reader knows a definition of map.
- The reader knows a definition of closure of subset of topological space.
Target Context
- The reader will have a definition of support of map from topological space into ring or module.
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:
\( T\): \(\in \{\text{ the topological spaces }\}\)
\( S\): \(\in \{\text{ the rings }\} \cup \{\text{ the modules }\}\)
\( f\): \(: T \to S\)
\(*supp f\): \(= \overline{f^{-1} (S \setminus \{0\})}\), where the over line denotes taking the closure
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Conditions:
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2: Note
The domain needs to be a topological space, because otherwise, the closure would not make sense; the codomain needs to be a ring or a module, because otherwise, \(0\) would not make sense.
