RT Journal Article
T1 On the semialgebraic Stone-Čech compactification of a semialgebraic set
A1 Fernando Galván, José Francisco
A1 Gamboa Mutuberria, José Manuel
AB In the same vein as the classical Stone–ˇCech compactification, we prove in this work that the maximal spectra of the rings of semialgebraic and bounded semialgebraic functions on a semialgebraic set M ⊂ Rn, which are homeomorphic topological spaces, provide the smallest Hausdorff compactification of M such that each bounded R-valued semialgebraic function on M extends continuously to it. Such compactification β∗sM, which can be characterized as the smallest compactification that dominates all semialgebraic compactifications of M, is called the semialgebraic Stone– ˇ Cech compactification of M, although it is very rarely a semialgebraic set. We are also interested in determining the main topological properties of the remainder ∂M = β∗sM \M and we prove that it has finitely many connected components and that this number equals the number of connected components of the remainder of a suitable semialgebraic compactification of M. Moreover, ∂M is locally connected and its local compactness can be characterized just in terms of the topology of M.
PB American Mathematical Society
SN 1088-6850
YR 2012
FD 2012
LK https://hdl.handle.net/20.500.14352/42296
UL https://hdl.handle.net/20.500.14352/42296
LA eng
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NO Banco de Santander
NO Universidad Complutense de Madrid
DS Docta Complutense
RD 4 may 2024