818: Support of Map from Topological Space into Ring or Module

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definition of support of map from topological space into ring or module

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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: Note

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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.

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Target Context

• The reader will have a definition of support of map from topological space into ring or module.

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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:
$T$: $\in \{\text{ the topological spaces }\}$
$S$: $\in \{\text{ the rings }\}\cup \{\text{ the modules }\}$
$f$: $:T\to S$
$\ast suppf$: $=\overline{f^{-1}(S\setminus \{0\})}$, 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.

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References

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