Displaying similar documents to “Rigid subanalytic sets”

Absolutely strongly star-Hurewicz spaces

Yan-Kui Song (2015)

Open Mathematics

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A space X is absolutely strongly star-Hurewicz if for each sequence (Un :n ∈ℕ/ of open covers of X and each dense subset D of X, there exists a sequence (Fn :n ∈ℕ/ of finite subsets of D such that for each x ∈X, x ∈St(Fn; Un) for all but finitely many n. In this paper, we investigate the relationships between absolutely strongly star-Hurewicz spaces and related spaces, and also study topological properties of absolutely strongly star-Hurewicz spaces.

Remarks on strongly star-Menger spaces

Yan-Kui Song (2013)

Commentationes Mathematicae Universitatis Carolinae

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A space X is strongly star-Menger if for each sequence ( 𝒰 n : n ∈ ℕ ) of open covers of X , there exists a sequence ( K n : n ∈ N ) of finite subsets of X such that { S t ( K n , 𝒰 n ) : n ∈ ℕ } is an open cover of X . In this paper, we investigate the relationship between strongly star-Menger spaces and related spaces, and also study topological properties of strongly star-Menger spaces.

A generic condition implying o-minimality for restricted C ∞ -functions

Olivier Le Gal (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

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We prove that the expansion of the real field by a restricted C ∞ -function is generically o-minimal. Such a result was announced by A. Grigoriev, and proved in a different way. Here, we deduce quasi-analyticity from a transcendence condition on Taylor expansions. This then implies o-minimality. The transcendance condition is shown to be generic. As a corollary, we recover in a simple way that there exist o-minimal structures that doesn’t admit analytic cell decomposition, and that there...