support of function
Definition Suppose is a topological space, and is a function. Then the support of (written as ), is the set
In other words, is the closure of the set where does not vanish.
Properties
Let be a function.
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1.
is closed.
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2.
If , then .
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3.
If , then .
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4.
If is such that on , then .
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5.
If are functions, then we have
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6.
If is another topological space, and is a homeomorphism, then
Title | support of function |
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Canonical name | SupportOfFunction |
Date of creation | 2013-03-22 13:46:10 |
Last modified on | 2013-03-22 13:46:10 |
Owner | matte (1858) |
Last modified by | matte (1858) |
Numerical id | 16 |
Author | matte (1858) |
Entry type | Definition |
Classification | msc 54-00 |
Synonym | support |
Synonym | carrier |
Related topic | ZeroOfAFunction |
Related topic | ApplicationsOfUrysohnsLemmaToLocallyCompactHausdorffSpaces |