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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S. Moll (2008)
Banach Center Publications
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Let X be a completely regular Hausdorff topological space and the space of continuous real-valued maps on X endowed with the pointwise topology. A simple and natural argument is presented to show how to construct on the space , if X contains a homeomorphic copy of the closed interval [0,1], real-valued maps which are everywhere discontinuous but continuous on all compact subsets of .
Stefan Geschke (2018)
Commentationes Mathematicae Universitatis Carolinae
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We consider dynamical systems of the form where is a compact metric space and is either a continuous map or a homeomorphism and provide a new proof that there is no universal metric dynamical system of this kind. The same is true for metric minimal dynamical systems and for metric abstract -limit sets, answering a question by Will Brian.
Vitalij A. Chatyrko (2021)
Commentationes Mathematicae Universitatis Carolinae
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In this paper the following two propositions are proved: (a) If , , is an infinite system of connected spaces such that infinitely many of them are nondegenerated completely Hausdorff topological spaces then the box product can be decomposed into continuum many disjoint nonempty open subsets, in particular, it is disconnected. (b) If , , is an infinite system of Brown Hausdorff topological spaces then the box product is also Brown Hausdorff, and hence, it is connected. A space...
Zbigniew Duszyński (2007)
Bollettino dell'Unione Matematica Italiana
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Richness of the class of -maps [3] is investigated. Several consequences for the theory of quasi--closed spaces are indicated.
Ludwik Jaksztas (2007)
Bulletin of the Polish Academy of Sciences. Mathematics
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This paper is motivated by the problem of dependence of the Hausdorff dimension of the Julia-Lavaurs sets for the map f₀(z) = z²+1/4 on the parameter σ. Using homographies, we imitate the construction of the iterated function system (IFS) whose limit set is a subset of , given by Urbański and Zinsmeister. The closure of the limit set of our IFS is the closure of some family of circles, and if the parameter σ varies, then the behavior of the limit set is similar to the behavior of...
Sumit Chandok, Arslan Hojjat Ansari, Tulsi Dass Narang (2019)
Mathematica Bohemica
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We introduce partial generalized convex contractions of order and rank using some auxiliary functions. We present some results on approximate fixed points and fixed points for such class of mappings having no continuity condition in -complete metric spaces and -complete metric spaces. Also, as an application, some fixed point results in a metric space endowed with a binary relation and some approximate fixed point results in a metric space endowed with a graph have been obtained....
Ivan Lončar (2017)
Archivum Mathematicum
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For metrizable continua, there exists the well-known notion of a Whitney map. If is a nonempty, compact, and metric space, then any Whitney map for any closed subset of can be extended to a Whitney map for [3, 16.10 Theorem]. The main purpose of this paper is to prove some generalizations of this theorem.
Sophocles K. Mercourakis, Vassiliadis G. Vassiliadis (2018)
Commentationes Mathematicae Universitatis Carolinae
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Let be a bounded countable metric space and a constant, such that , for any pairwise distinct points of . For such metric spaces we prove that they can be isometrically embedded into any Banach space containing an isomorphic copy of .
Tomasz Szarek, Maciej Ślęczka (2006)
Bulletin of the Polish Academy of Sciences. Mathematics
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It is shown that every Polish space X with admits a compact subspace Y such that where and denote the topological and Hausdorff dimensions, respectively.
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.
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...
Dmitri Shakhmatov, Michael Tkachenko (2002)
Fundamenta Mathematicae
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Topologies τ₁ and τ₂ on a set X are called T₁-complementary if τ₁ ∩ τ₂ = X∖F: F ⊆ X is finite ∪ ∅ and τ₁∪τ₂ is a subbase for the discrete topology on X. Topological spaces and are called T₁-complementary provided that there exists a bijection f: X → Y such that and are T₁-complementary topologies on X. We provide an example of a compact Hausdorff space of size which is T₁-complementary to itself ( denotes the cardinality of the continuum). We prove that the existence of a compact...
Alessandro Perotti (1986)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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Viene studiata l'equazione per le forme regolari sulla chiusura dell'intersezione di domini pseudoconvessi. Si costruisce un operatore soluzione in forma integrale e sotto ipotesi opportune si ottengono stime della soluzione nelle norme .
D. Sivaraj, V. Renuka Devi (2007)
Bollettino dell'Unione Matematica Italiana
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We introduce a new class of spaces, called Hausdorff modulo or mod spaces with respect to an ideal which contains the class of all Hausdorff spaces. Characterizations of these spaces are given and their properties are investigated. The concept of compactness modulo an ideal was introduced by Newcomb in 1967 and studied by Hamlett and Jankovic in 1990. We study the properties of -compact subsets in Hausdorff modulo spaces and generalize some results of Hamlett and Jankovic....
Lois Kailhofer (2003)
Fundamenta Mathematicae
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We work within the one-parameter family of symmetric tent maps, where the slope is the parameter. Given two such tent maps , with periodic critical points, we show that the inverse limit spaces and are not homeomorphic when a ≠ b. To obtain our result, we define topological substructures of a composant, called “wrapping points” and “gaps”, and identify properties of these substructures preserved under a homeomorphism.
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.
Angelo Bella, Biagio Ricceri (1983)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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In questa Nota, dati uno spazio metrico perfetto ed un suo sottoinsieme chiuso e raro, si dimostra l'esistenza di una funzione continua tale che per ogni , per ogni e per qualche . In particolare, ciò permette di dare risposta simultaneamente a due questioni poste in [2]. Si mettono in evidenza, poi, ulteriori conseguenze di tale risultato.
Ludwik Jaksztas (2011)
Fundamenta Mathematicae
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Let f₀(z) = z²+1/4. We denote by ₀ the set of parameters σ ∈ ℂ for which the critical point 0 escapes from the filled-in Julia set K(f₀) in one step by the Lavaurs map . We prove that if σ₀ ∈ ∂₀, then the Hausdorff dimension of the Julia-Lavaurs set is continuous at σ₀ as the function of the parameter if and only if . Since on a dense set of parameters which correspond to preparabolic points, the lower semicontinuity implies the continuity of on an open and dense subset of...
Jozef Myjak, Tomasz Szarek (2002)
Fundamenta Mathematicae
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Let X be a locally compact, separable metric space. We prove that , where and stand for the concentration dimension and the topological dimension of X, respectively.