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Ramsey Theorems and the Property of Baire

Bernd Voigt (1985)

Publications du Département de mathématiques (Lyon)

Ramsey-like properties for bi-Lipschitz mappings of finite metric spaces

Jiří Matoušek (1992)

Commentationes Mathematicae Universitatis Carolinae

Let $(X, ρ)$ , $(Y, σ)$ be metric spaces and $f : X \to Y$ an injective mapping. We put ${∥ f ∥}_{L i p} = sup {σ (f (x), f (y)) / ρ (x, y)$ ; $x, y \in X$ , $x \neq y}$ , and $dist (f) = {∥ f ∥}_{L i p} . {∥ f^{- 1} ∥}_{L i p}$ (the distortion of the mapping $f$ ). Some Ramsey-type questions for mappings of finite metric spaces with bounded distortion are studied; e.g., the following theorem is proved: Let $X$ be a finite metric space, and let $ε > 0$ , $K$ be given numbers. Then there exists a finite metric space $Y$ , such that for every mapping $f : Y \to Z$ ( $Z$ arbitrary metric space) with $dist (f) < K$ one can find a mapping $g : X \to Y$ , such that both the mappings $g$ and ${f |}_{g (X)}$ have distortion at...

Rational extensions of C(X) and semicontinuous functions [Book]

Jürg Schmid (1988)

Real complete and K-complete proximity

Alo, R.A., Talamo, R. (1978)

Portugaliae mathematica

Real maximal round filters in proximity spaces

Don Mattson (1973)

Fundamenta Mathematicae

Real-valued functions on Alexandroff (zero-set) spaces

Anthony W. Hager (1975)

Commentationes Mathematicae Universitatis Carolinae

Real-valued functions on certain semi-metric spaces

Harold R. Bennett (1975)

Compositio Mathematica

Recent developments in the theory of Borel reducibility

Greg Hjorth, Alexander S. Kechris (2001)

Fundamenta Mathematicae

Let E₀ be the Vitali equivalence relation and E₃ the product of countably many copies of E₀. Two new dichotomy theorems for Borel equivalence relations are proved. First, for any Borel equivalence relation E that is (Borel) reducible to E₃, either E is reducible to E₀ or else E₃ is reducible to E. Second, if E is a Borel equivalence relation induced by a Borel action of a closed subgroup of the infinite symmetric group that admits an invariant metric, then either E is reducible to a countable...

Recent research in hyperspace theory.

Janusz J. Charatonik (2003)

Extracta Mathematicae

Reconstruction of manifolds and subsets of normed spaces from subgroups of their homeomorphism groups [Book]

Matatyahu Rubin, Yosef Yomdin (2005)

Recouvrements, derivation des mesures et dimensions.

Patrice Assouad, Thierry Quentin de Gromard (2006)

Revista Matemática Iberoamericana

Let X be a set with a symmetric kernel d (not necessarily a distance). The space (X,d) is said to have the weak (resp. strong) covering property of degree ≤ m [briefly prf(m) (resp. prF(m))], if, for each family B of closed balls of (X,d) with radii in a decreasing sequence (resp. with bounded radii), there is a subfamily, covering the center of each element of B, and of order ≤ m (resp. splitting into m disjoint families). Since Besicovitch, covering properties are known to be the main tool for...

Rectangular covers of products missing diagonals

Yukinobu Yajima (1994)

Commentationes Mathematicae Universitatis Carolinae

We give a characterization of a paracompact $Σ$ -space to have a $G_{δ}$ -diagonal in terms of three rectangular covers of $X^{2} ∖ Δ$ . Moreover, we show that a local property and a global property of a space $X$ are given by the orthocompactness of $(X \times β X) ∖ Δ$ .

Refinable maps

Jo Ford, J. W. Rogers, Jr. (1978)

Colloquium Mathematicae

Reflections not preserving completeness

Pelant, Jan (1975)

Seminar Uniform Spaces

Reflections on distal spaces

Vilímovský, Jiří (1976)

Seminar Uniform Spaces

Reflective and coreflective subcategories of Unif (and Top)

Hušek, Miroslav (1975)

Seminar Uniform Spaces

Reflective functors via nearness

S. Naimpally (1974)

Fundamenta Mathematicae

Reflexive families of closed sets

Zhongqiang Yang, Dongsheng Zhao (2006)

Fundamenta Mathematicae

Let S(X) denote the set of all closed subsets of a topological space X, and C(X) the set of all continuous mappings f:X → X. A family 𝓐 ⊆ S(X) is called reflexive if there exists ℱ ⊆ C(X) such that 𝓐 = {A ∈ S(X): f(A) ⊆ A for every f ∈ ℱ}. We investigate conditions ensuring that a family of closed subsets is reflexive.

Regular and Other Kinds of Extensions of Topological Spaces

Dimov, G. (1998)

Serdica Mathematical Journal

∗ This work was partially supported by the National Foundation for Scientific Researches at the Bulgarian Ministry of Education and Science under contract no. MM-427/94.In this paper the notion of SR-proximity is introduced and in virtue of it some new proximity-type descriptions of the ordered sets of all (up to equivalence) regular, resp. completely regular, resp. locally compact extensions of a topological space are obtained. New proofs of the Smirnov Compactification Theorem [31] and of the...

Regular mappings between dimensions

Guy David, Stephen Semmes (2000)

Publicacions Matemàtiques

The notions of Lipschitz and bilipschitz mappings provide classes of mappings connected to the geometry of metric spaces in certain ways. A notion between these two is given by regular mappings (reviewed in Section 1), in which some non-bilipschitz behavior is allowed, but with limitations on this, and in a quantitative way. In this paper we look at a class of mappings called (s, t)-regular mappings. These mappings are the same as ordinary regular mappings when s = t, but otherwise they behave somewhat...

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