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- W2952807029 abstract "In this work we analyze some topological properties of the remainder $partial M:=beta_s^* Msetminus M$ of the semialgebraic Stone-Cv{e}ch compactification $beta_s^* M$ of a semialgebraic set $Msubset{mathbb R}^m$ 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 $M_{rm lc}cup( {rm Cl}_{beta_s^* M}(overline{M}_{leq1})setminusoverline{M}_{leq1})$ where $M_{rm lc}$ is the largest locally compact dense subset of $M$ and $overline{M}_{leq1}$ is the closure in $M$ of the set of $1$-dimensional points of $M$. In addition, we analyze the properties of the sets $widehat{partial}M$ and $widetilde{partial}M$ of free maximal ideals associated with formal and semialgebraic paths. We prove that both are dense subsets of the remainder $partial M$ and that the differences $partial Msetminuswidehat{partial}M$ and $widehat{partial} Msetminuswidetilde{partial}M$ are also dense subsets of $partial M$. It holds moreover that all the points of $widehat{partial}M$ have countable systems of neighborhoods in $beta_s^* M$." @default.
- W2952807029 created "2019-06-27" @default.
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- W2952807029 date "2015-03-25" @default.
- W2952807029 modified "2023-10-14" @default.
- W2952807029 title "On the remainder of the semialgebraic Stone-Cv{e}ch compactification of a semialgebraic set" @default.
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- W2952807029 doi "https://doi.org/10.48550/arxiv.1503.07567" @default.
- W2952807029 hasPublicationYear "2015" @default.
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