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.

On the metric reflection of a pseudometric space in ZF

Horst Herrlich, Kyriakos Keremedis (2015)

Commentationes Mathematicae Universitatis Carolinae

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We show: (i) The countable axiom of choice 𝐂𝐀𝐂 is equivalent to each one of the statements: (a) a pseudometric space is sequentially compact iff its metric reflection is sequentially compact, (b) a pseudometric space is complete iff its metric reflection is complete. (ii) The countable multiple choice axiom 𝐂𝐌𝐂 is equivalent to the statement: (a) a pseudometric space is Weierstrass-compact iff its metric reflection is Weierstrass-compact. (iii) The axiom of choice 𝐀𝐂 is equivalent to each...

Properties of one-point completions of a noncompact metrizable space

Melvin Henriksen, Ludvík Janoš, Grant R. Woods (2005)

Commentationes Mathematicae Universitatis Carolinae

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If a metrizable space X is dense in a metrizable space Y , then Y is called a of X . If T 1 and T 2 are metric extensions of X and there is a continuous map of T 2 into T 1 keeping X pointwise fixed, we write T 1 ≤ T 2 . If X is noncompact and metrizable, then ( ℳ ( X ) , ≤ ) denotes the set of metric extensions of X , where T 1 and T 2 are identified if T 1 ≤ T 2 and T 2 ≤ T 1 , i.e., if there is a homeomorphism of T 1 onto T 2 keeping X pointwise fixed. ( ℳ ( X ) , ≤ ) is a large complicated poset studied extensively by V. Bel’nov [, Trans. Moscow Math....