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Fernando Galván, José Francisco and Gamboa, J. M. (2018) On the remainder of the semialgebraic StoneCech compactification of a semialgebraic set. Journal of Pure and Applied Algebra, 222 (1). pp. 118. ISSN 00224049

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Official URL: http://www.sciencedirect.com/science/article/pii/S0022404917300373
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Abstract
In this work we analyze some topological properties of the remainder partial derivative M := beta(s)*M\M of the semialgebraic StoneCech compactification beta(s)*M of a semialgebraic set M subset of Rm in order to 'distinguish' its points from those of M. To that end we prove that the set of points of beta(s)*M that admit a metrizable neighborhood in beta(s)*M equals M1c boolean OR (Cl beta(s)*M((M) over bar <= 1)\(M) over bar <= 1) where M1c is the largest locally compact dense subset of M and (M) over bar <= 1 is the closure in M of the set of 1dimensional points of M. In addition, we analyze the properties of the sets (partial derivative) over capM and (partial derivative) over tildeM of free maximal ideals associated with formal and semialgebraic paths. We prove that both are dense subsets of the remainder partial derivative M and that the differences partial derivative M\(partial derivative) over capM and (partial derivative) over capM\(partial derivative) over tildeM are also dense subsets of partial derivative M. It holds moreover that all the points of (partial derivative) over capM have countable systems of neighborhoods in beta(s)*M.
Item Type:  Article 

Uncontrolled Keywords:  Rings; Spaces 
Subjects:  Sciences > Mathematics > Geometry Sciences > Mathematics > Algebraic geometry 
ID Code:  45513 
Deposited On:  27 Nov 2017 10:16 
Last Modified:  10 May 2018 08:08 
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