On the tangency of sets in generalized metric spaces for certain functions of the class
T. Konik (1991)
Matematički Vesnik
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T. Konik (1991)
Matematički Vesnik
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Jacek Tabor (2002)
Mathematica Bohemica
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We give a meaning to derivative of a function , where is a complete metric space. This enables us to investigate differential equations in a metric space. One can prove in particular Gronwall’s Lemma, Peano and Picard Existence Theorems, Lyapunov Theorem or Nagumo Theorem in metric spaces. The main idea is to define the tangent space of . Let , be continuous at zero. Then by the definition and are in the same equivalence class if they are tangent at zero, that is if By...
Rodrigo Hernández-Gutiérrez, Paul J. Szeptycki (2015)
Fundamenta Mathematicae
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Given a metric space ⟨X,ρ⟩, consider its hyperspace of closed sets CL(X) with the Wijsman topology . It is known that is metrizable if and only if X is separable, and it is an open question by Di Maio and Meccariello whether this is equivalent to being normal. We prove that if the weight of X is a regular uncountable cardinal and X is locally separable, then is not normal. We also solve some questions by Cao, Junnila and Moors regarding isolated points in Wijsman hyperspaces. ...
Olli Tapiola (2016)
Colloquium Mathematicae
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With the help of recent adjacent dyadic constructions by Hytönen and the author, we give an alternative proof of results of Lechner, Müller and Passenbrunner about the -boundedness of shift operators acting on functions where 1 < p < ∞, X is a metric space and E is a UMD space.
Vincent Colin, Sheila Sandon (2015)
Journal of the European Mathematical Society
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We define an integer-valued non-degenerate bi-invariant metric (the discriminant metric) on the universal cover of the identity component of the contactomorphism group of any contact manifold. This metric has a very simple geometric definition, based on the notion of discriminant points of contactomorphisms. Using generating functions we prove that the discriminant metric is unbounded for the standard contact structures on and . On the other hand we also show by elementary arguments...
Agnieszka Bogdewicz, Jerzy Grzybowski (2009)
Banach Center Publications
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Let be a Minkowski space with a unit ball and let be the Hausdorff metric induced by in the hyperspace of convex bodies (nonempty, compact, convex subsets of ℝ). R. Schneider [RSP] characterized pairs of elements of which can be joined by unique metric segments with respect to for the Euclidean unit ball Bⁿ. We extend Schneider’s theorem to the hyperspace over any two-dimensional Minkowski space.
Yasushi Hirata (2015)
Commentationes Mathematicae Universitatis Carolinae
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In [The sup = max problem for the extent of generalized metric spaces, Comment. Math. Univ. Carolin. The special issue devoted to Čech 54 (2013), no. 2, 245–257], the author and Yajima discussed the sup = max problem for the extent and the Lindelöf degree of generalized metric spaces: (strict) -spaces, (strong) -spaces and semi-stratifiable spaces. In this paper, the sup = max problem for the Lindelöf degree of spaces having -diagonals and for the extent of spaces having point-countable...
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.
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.
Eleftherios Tachtsis (2010)
Bulletin of the Polish Academy of Sciences. Mathematics
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We work in ZF set theory (i.e., Zermelo-Fraenkel set theory minus the Axiom of Choice AC) and show the following: 1. The Axiom of Choice for well-ordered families of non-empty sets () does not imply “the Tychonoff product , where 2 is the discrete space 0,1, is countably compact” in ZF. This answers in the negative the following question from Keremedis, Felouzis, and Tachtsis [Bull. Polish Acad. Sci. Math. 55 (2007)]: Does the Countable Axiom of Choice for families of non-empty sets...