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| In [[mathematics]], especially in [[real algebraic geometry]], a '''semialgebraic space''' is a space which is locally isomorphic to a [[semialgebraic set]].
| | I am Kristopher from Gjovik. I am learning to play the Lap Steel Guitar. Other hobbies are Crocheting.<br><br>My web-site [http://sciencestage.com/out/out.php?url=http://beardtrimmerblog.wordpress.com/2014/10/15/beard-trimmers/ beard beads] |
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| ==Definition==
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| Let ''U'' be an open subset of '''R'''<sup>''n''</sup> for some ''n''. A '''semialgebraic function''' on ''U'' is defined to be a [[continuous function|continuous]] [[real number|real]]-valued function on ''U'' whose restriction to any [[semialgebraic set]] contained in ''U'' has a [[graph of a function|graph]] which is a semialgebraic subset of the product space '''R'''<sup>''n''</sup>×'''R'''. This endows '''R'''<sup>''n''</sup> with a sheaf <math>\mathcal{O}_{\mathbf{R}^n}</math> of semialgebraic functions.
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| (For example, any polynomial mapping between semialgebraic sets is a semialgebraic function, as is the maximum of two semialgebraic functions.)
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| A '''semialgebraic space''' is a [[locally ringed space]] <math>(X, \mathcal{O}_X)</math> which is locally isomorphic to '''R'''<sup>''n''</sup> with its sheaf of semialgebraic functions.
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| ==See also==
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| *[[Semialgebraic set]]
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| *[[Real algebraic geometry]]
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| *[[Real closed ring]]
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| {{geometry-stub}}
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| [[Category:Real algebraic geometry]]
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Latest revision as of 14:25, 13 December 2014
I am Kristopher from Gjovik. I am learning to play the Lap Steel Guitar. Other hobbies are Crocheting.
My web-site beard beads