Displaying similar documents to “Functor of extension of Λ -isometric maps between central subsets of the unbounded Urysohn universal space”

The Banach contraction mapping principle and cohomology

Ludvík Janoš (2000)

Commentationes Mathematicae Universitatis Carolinae

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By a dynamical system ( X , T ) we mean the action of the semigroup ( ℤ + , + ) on a metrizable topological space X induced by a continuous selfmap T : X → X . Let M ( X ) denote the set of all compatible metrics on the space X . Our main objective is to show that a selfmap T of a compact space X is a Banach contraction relative to some d 1 ∈ M ( X ) if and only if there exists some d 2 ∈ M ( X ) which, regarded as a 1 -cocycle of the system ( X , T ) × ( X , T ) , is a coboundary.

Central subsets of Urysohn universal spaces

Piotr Niemiec (2009)

Commentationes Mathematicae Universitatis Carolinae

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A subset A of a metric space ( X , d ) is central iff for every Katětov map f : X → ℝ upper bounded by the diameter of X and any finite subset B of X there is x ∈ X such that f ( a ) = d ( x , a ) for each a ∈ A ∪ B . Central subsets of the Urysohn universal space 𝕌 (see introduction) are studied. It is proved that a metric space X is isometrically embeddable into 𝕌 as a central set iff X has the collinearity property. The Katětov maps of the real line are characterized.

Metric enrichment, finite generation, and the path coreflection

Alexandru Chirvasitu (2024)

Archivum Mathematicum

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We prove a number of results involving categories enriched over CMet, the category of complete metric spaces with possibly infinite distances. The category CPMet of path complete metric spaces is locally ℵ 1 -presentable, closed monoidal, and coreflective in CMet. We also prove that the category CCMet of convex complete metric spaces is not closed monoidal and characterize the isometry- ℵ 0 -generated objects in CMet, CPMet and CCMet, answering questions by Di Liberti and Rosický. Other results...

A generalization of boundedly compact metric spaces

Gerald Beer, Anna Di Concilio (1991)

Commentationes Mathematicae Universitatis Carolinae

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A metric space 〈 X , d 〉 is called a UC space provided each continuous function on X into a metric target space is uniformly continuous. We introduce a class of metric spaces that play, relative to the boundedly compact metric spaces, the same role that UC spaces play relative to the compact metric spaces.