A class of retracts in with some applications to differential inclusion
Grzegorz Bartuzel, Andrzej Fryszkowski (2002)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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Grzegorz Bartuzel, Andrzej Fryszkowski (2002)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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A. Chigogidze (2013)
Fundamenta Mathematicae
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We characterize, in terms of X, the extensional dimension of the Stone-Čech corona βX∖X of a locally compact and Lindelöf space X. The non-Lindelöf case is also settled in terms of extending proper maps with values in , where L is a finite complex. Further, for a finite complex L, an uncountable cardinal τ and a -set X in the Tikhonov cube we find a necessary and sufficient condition, in terms of , for X to be in the class AE([L]). We also introduce a concept of a proper absolute...
Lucie Loukotová (2017)
Commentationes Mathematicae Universitatis Carolinae
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The aim of this paper is to introduce a generalization of the classical absolute continuity to a relative case, with respect to a subset of an interval . This generalization is based on adding more requirements to disjoint systems from the classical definition of absolute continuity – these systems should be not too far from and should be small relative to some covers of . We discuss basic properties of relative absolutely continuous functions and compare this class with other...
Rodrigo Hidalgo Linares, Oleg Okunev (2023)
Commentationes Mathematicae Universitatis Carolinae
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We study the relation of -equivalence defined between Tychonoff spaces, that is, we study the topological isomorphisms of their respective free locally convex spaces. We introduce the concept of an -retract in a Tychonoff space in terms of the existence of a special kind of simultaneous extensions of continuous functions, explore the relation of this concept with the Dugundji extension theorem, and find some conditions that allow us to identify -retracts in various classes of topological...
Dayan Liu, Xiaosong Sun (2022)
Czechoslovak Mathematical Journal
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Let be a field of characteristic zero and a -domain. Let be a retract of being the kernel of a locally nilpotent derivation of . We show that if for some principal ideal (in particular, if is a UFD), then , i.e., is a polynomial algebra over in one variable. It is natural to ask that, if a retract of a -UFD is the kernel of two commuting locally nilpotent derivations of , then does it follow that ? We give a negative answer to this question. The interest in...
Jiří Matoušek, Martin Tancer, Uli Wagner (2011)
Journal of the European Mathematical Society
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Let be the following algorithmic problem: Given a finite simplicial complex of dimension at most , does there exist a (piecewise linear) embedding of into ? Known results easily imply polynomiality of (; the case is graph planarity) and of for all . We show that the celebrated result of Novikov on the algorithmic unsolvability of recognizing the 5-sphere implies that and are undecidable for each . Our main result is NP-hardness of and, more generally, of for all...
Franklin D. Tall (2002)
Fundamenta Mathematicae
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Given a topological space ⟨X,⟩ ∈ M, an elementary submodel of set theory, we define to be X ∩ M with topology generated by . Suppose is homeomorphic to the irrationals; must ? We have partial results. We also answer a question of Gruenhage by showing that if is homeomorphic to the “Long Cantor Set”, then .
Ziqin Feng (2021)
Commentationes Mathematicae Universitatis Carolinae
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We say that a collection of subsets of has property if there is a set and point-countable collections of closed subsets of such that for any there is a finite subcollection of such that . Then we prove that any compact space is Corson if and only if it has a point-- base. A characterization of Corson compacta in terms of (strong) point network is also given. This provides an answer to an open question in “A Biased View of Topology as a Tool in Functional Analysis”...
Alireza Abdollahi, Javad Bagherian, Mahdi Ebrahimi, Maryam Khatami, Zahra Shahbazi, Reza Sobhani (2022)
Czechoslovak Mathematical Journal
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For a complex character of a finite group , it is known that the product is a multiple of , where is the image of on . The character is said to be a sharp character of type if and . If the principal character of is not an irreducible constituent of , then the character is called normalized. It is proposed as a problem by P. J. Cameron and M. Kiyota, to find finite groups with normalized sharp characters of type . Here we prove that such a group with nontrivial...
Aleksander V. Arhangel'skii (2019)
Commentationes Mathematicae Universitatis Carolinae
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It is shown that there exists a -compact topological group which cannot be represented as a continuous image of a Lindelöf -group, see Example 2.8. This result is based on an inequality for the cardinality of continuous images of Lindelöf -groups (Theorem 2.1). A closely related result is Corollary 4.4: if a space is a continuous image of a Lindelöf -group, then there exists a covering of by dyadic compacta such that . We also show that if a homogeneous compact space is...
D. E. Edmunds, V. B. Moscatelli
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CONTENTSIntroduction............................................................................................................ 51. Preliminaries............................................................................................................. 82. Embedding into into (n>1).......................................... 103. The case n = 1.......................................................................................................... 284. Embedding into ...............................................................
Th. Friedrich (1974)
Colloquium Mathematicae
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Christian Samuel (2010)
Colloquium Mathematicae
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We show that every operator from to is compact when 1 ≤ p,q < s and that every operator from to is compact when 1/p + 1/q > 1 + 1/s.
D. W. Hajek, I. Irizarry (1981)
Matematički Vesnik
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Sergei Logunov (2022)
Commentationes Mathematicae Universitatis Carolinae
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Let a space be Tychonoff product of -many Tychonoff nonsingle point spaces . Let Suslin number of be strictly less than the cofinality of . Then we show that every point of remainder is a non-normality point of its Čech–Stone compactification . In particular, this is true if is either or and a cardinal is infinite and not countably cofinal.
J. Musiałek (1969)
Annales Polonici Mathematici
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Tadeusz Dobrowolski, Witold Marciszewski (2002)
Fundamenta Mathematicae
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In every infinite-dimensional Fréchet space X, we construct a linear subspace E such that E is an -subset of X and contains a retract R so that is not homeomorphic to . This shows that Toruńczyk’s Factor Theorem fails in the Borel case.
Hisao Kato, Eiichi Matsuhashi (2006)
Colloquium Mathematicae
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The first author has recently proved that if f: X → Y is a k-dimensional map between compacta and Y is p-dimensional (0 ≤ k, p < ∞), then for each 0 ≤ i ≤ p + k, the set of maps g in the space such that the diagonal product is an (i+1)-to-1 map is a dense -subset of . In this paper, we prove that if f: X → Y is as above and (j = 1,..., k) are superdendrites, then the set of maps h in such that is (i+1)-to-1 is a dense -subset of for each 0 ≤ i ≤ p.
Tomasz Słonka (2012)
Colloquium Mathematicae
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We show that if n is a positive integer and , then for every positive integer m and for every real constant c > 0 there are functions such that and for every x ∈ ℝⁿ there exists a strictly increasing sequence (i₁,...,iₙ) of numbers from 1,...,n+m and a w ∈ ℤⁿ such that for .
Jean Saint Raymond (2007)
Fundamenta Mathematicae
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Let X be a Polish space, and let C₀ and C₁ be disjoint coanalytic subsets of X. The pair (C₀,C₁) is said to be complete if for every pair (D₀,D₁) of disjoint coanalytic subsets of there exists a continuous function such that and . We give several explicit examples of complete pairs of coanalytic sets.
Joseph Kupka
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CONTENTS1. Introduction...................................................................................................... 52. Notation and basic terminology........................................................................... 73. Definition and basic properties of the spaces................................. 114. Integral representation of bounded linear functionals on ........ 235. Examples in theory...................................................................................
Krzysztof Kołodziejczyk (1987)
Colloquium Mathematicae
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Hans Triebel (1994)
Studia Mathematica
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Let , where the sum is taken over the lattice of all points k in having integer-valued components, j∈ℕ and . Let be either or (s ∈ ℝ, 0 < p < ∞, 0 < q ≤ ∞) on The aim of the paper is to clarify under what conditions is equivalent to .