RT Journal Article
T1 On the remainder of the semialgebraic Stone-Cech compactification of a semialgebraic set
A1 Fernando Galván, José Francisco
A1 Gamboa Mutuberria, José Manuel
AB In this work we analyze some topological properties of the remainder partial derivative M := beta(s)*M\M of the semialgebraic Stone-Cech compactification beta(s)*M of a semialgebraic set M subset of R-m 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 M-1c boolean OR (Cl beta(s)*M((M) over bar <= 1)\(M) over bar <= 1) where M-1c is the largest locally compact dense subset of M and (M) over bar <= 1 is the closure in M of the set of 1-dimensional 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.
PB Elsevier Science B.V. (North-Holland)
SN 0022-4049
YR 2018
FD 2018
LK https://hdl.handle.net/20.500.14352/18252
UL https://hdl.handle.net/20.500.14352/18252
LA eng
NO Ministerio de Ciencia e Innovación (MICINN)
NO Universidad Complutense de Madrid
NO GAAR Grupos
DS Docta Complutense
RD 4 may 2024