Precompact contraction of metric uniformities, and the continuity of
C. J. Himmelberg (1973)
Rendiconti del Seminario Matematico della Università di Padova
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C. J. Himmelberg (1973)
Rendiconti del Seminario Matematico della Università di Padova
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Giovanni Anello, Paolo Cubiotti (2004)
Annales Polonici Mathematici
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We consider a multifunction , where T, X and E are separable metric spaces, with E complete. Assuming that F is jointly measurable in the product and a.e. lower semicontinuous in the second variable, we establish the existence of a selection for F which is measurable with respect to the first variable and a.e. continuous with respect to the second one. Our result is in the spirit of [11], where multifunctions of only one variable are considered.
Hôǹg Thái Nguyêñ, Maciej Juniewicz, Jolanta Ziemińska (2001)
Studia Mathematica
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We present a new continuous selection theorem, which unifies in some sense two well known selection theorems; namely we prove that if F is an H-upper semicontinuous multivalued map on a separable metric space X, G is a lower semicontinuous multivalued map on X, both F and G take nonconvex -decomposable closed values, the measure space T with a σ-finite measure μ is nonatomic, 1 ≤ p < ∞, is the Bochner-Lebesgue space of functions defined on T with values in a Banach space E, F(x)...
Gerald Beer, Anna Di Concilio (1991)
Commentationes Mathematicae Universitatis Carolinae
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A metric space is called a space provided each continuous function on 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 spaces play relative to the compact metric spaces.
Ludvík Janoš (2000)
Commentationes Mathematicae Universitatis Carolinae
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By a dynamical system we mean the action of the semigroup on a metrizable topological space induced by a continuous selfmap . Let denote the set of all compatible metrics on the space . Our main objective is to show that a selfmap of a compact space is a Banach contraction relative to some if and only if there exists some which, regarded as a -cocycle of the system , is a coboundary.
Nacereddine Belili, Henri Heinich (2001)
Applicationes Mathematicae
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We consider a Köthe space of random variables (r.v.) defined on the Lebesgue space ([0,1],B,λ). We show that for any sub-σ-algebra ℱ of B and for all r.v.’s X with values in a separable finitely compact metric space (M,d) such that d(X,x) ∈ for all x ∈ M (we then write X ∈ (M)), there exists a median of X given ℱ, i.e., an ℱ-measurable r.v. Y ∈ (M) such that for all ℱ-measurable Z. We develop the basic theory of these medians, we show the convergence of empirical medians and we give...
Bożena Piątek (2005)
Annales Polonici Mathematici
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A continuous multifunction F:[a,b] → clb(Y) is *-concave if and only if the inclusion holds for every s,t ∈ [a,b], s < t.
Horst Herrlich, Kyriakos Keremedis (2015)
Commentationes Mathematicae Universitatis Carolinae
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We show: (i) The countable axiom of choice 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 is equivalent to the statement: (a) a pseudometric space is Weierstrass-compact iff its metric reflection is Weierstrass-compact. (iii) The axiom of choice is equivalent to each...
Alberto Bressan, Giovanni Colombo (1992)
Studia Mathematica
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Let (X,T) be a paracompact space, Y a complete metric space, a lower semicontinuous multifunction with nonempty closed values. We prove that if is a (stronger than T) topology on X satisfying a compatibility property, then F admits a -continuous selection. If Y is separable, then there exists a sequence of -continuous selections such that for all x ∈ X. Given a Banach space E, the above result is then used to construct directionally continuous selections on arbitrary subsets...
T. Banakh, R. Voytsitskyy (2008)
Colloquium Mathematicae
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It is shown that the hyperspace (resp. ) of non-empty closed (resp. closed and bounded) subsets of a metric space (X,d) is homeomorphic to ℓ₂ if and only if the completion X̅ of X is connected and locally connected, X is topologically complete and nowhere locally compact, and each subset (resp. each bounded subset) of X is totally bounded.
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 -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--generated objects in CMet, CPMet and CCMet, answering questions by Di Liberti and Rosický. Other results...
Irmina Herburt, Maria Moszyńska, Dorette Pronk (2009)
Banach Center Publications
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In 1989 R. Arnold proved that for every pair (A,B) of compact convex subsets of ℝ there is an Euclidean isometry optimal with respect to L₂ metric and if f₀ is such an isometry, then the Steiner points of f₀(A) and B coincide. In the present paper we solve related problems for metrics topologically equivalent to the Hausdorff metric, in particular for metrics for all p ≥ 2 and the symmetric difference metric.