On connectivity properties of hyperspaces of spaces
M. Mršević (1979)
Matematički Vesnik
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M. Mršević (1979)
Matematički Vesnik
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Teo Mora (1989)
Publications mathématiques et informatique de Rennes
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S. Topa (1976)
Annales Polonici Mathematici
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Ziqin Feng, Paul Gartside (2013)
Fundamenta Mathematicae
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Necessary conditions and sufficient conditions are given for to be a (σ-) m₁- or m₃-space. (A space is an m₁-space if each of its points has a closure-preserving local base.) A compact uncountable space K is given with an m₁-space, which answers questions raised by Dow, Ramírez Martínez and Tkachuk (2010) and Tkachuk (2011).
Benjamín Espinoza, Verónica Martínez-de-la-Vega, Jorge M. Martínez-Montejano (2009)
Colloquium Mathematicae
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A hit-and-miss topology () is defined for the hyperspaces , Cₙ(X) and Fₙ(X) of a continuum X. We study the relationship between and the Vietoris topology and we find conditions on X for which these topologies are equivalent.
Jia Chao (1974)
Studia Mathematica
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Tosiya Miyasita, Takashi Suzuki (2004)
Banach Center Publications
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The non-local Gel’fand problem, with Dirichlet boundary condition, is studied on an n-dimensional bounded domain Ω. If it is star-shaped, then we have an upper bound of λ for the existence of the solution. We also have infinitely many bendings in λ of the connected component of the solution set in λ,v if Ω is a ball and 3 ≤ n ≤ 9.
Jonathan David Farley (2023)
Mathematica Bohemica
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Duffus wrote in his 1978 Ph.D. thesis, “It is not obvious that is connected and imply that is connected”, where and are finite nonempty posets. We show that, indeed, under these hypotheses is connected and .
Dachun Yang, Sibei Yang
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Let Φ be a concave function on (0,∞) of strictly critical lower type index and (the class of local weights introduced by V. S. Rychkov). We introduce the weighted local Orlicz-Hardy space via the local grand maximal function. Let for all t ∈ (0,∞). We also introduce the BMO-type space and establish the duality between and . Characterizations of , including the atomic characterization, the local vertical and the local nontangential maximal function characterizations, are...
F. Azarpanah, M. Paimann, A. R. Salehi (2015)
Commentationes Mathematicae Universitatis Carolinae
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In this article we define the -topology on some rings of quotients of . Using this, we equip the classical ring of quotients of with the -topology and we show that with the -topology is in fact a subspace of with the -topology. Characterization of the components of rings of quotients of is given and using this, it turns out that with the -topology is connected if and only if is a pseudocompact almost -space, if and only if with -topology is connected. We also...
Peixin Zhang, Mingxuan Zhu (2022)
Applications of Mathematics
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We establish the local-in-time existence of a solution to the non-resistive magneto-micropolar fluids with the initial data , and for and any . The initial regularity of the micro-rotational velocity is weaker than velocity of the fluid .
Michael Bildhauer, Martin Fuchs, Xiao Zhong (2007)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Starting from Giaquinta’s counterexample [12] we introduce the class of splitting functionals being of -growth with exponents and show for the scalar case that locally bounded local minimizers are of class . Note that to our knowledge the only -results without imposing a relation between and concern the case of two independent variables as it is outlined in Marcellini’s paper [15], Theorem A, and later on in the work of Fusco and Sbordone [10], Theorem 4.2.
José del Carmen Alberto-Domínguez, Gerardo Acosta, Maira Madriz-Mendoza (2022)
Commentationes Mathematicae Universitatis Carolinae
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A topological space is totally Brown if for each and every nonempty open subsets of we have . Totally Brown spaces are connected. In this paper we consider a topology on the set of natural numbers. We then present properties of the topological space , some of them involve the closure of a set with respect to this topology, while others describe subsets which are either totally Brown or totally separated. Our theorems generalize results proved by P. Szczuka in 2013, 2014,...
Dihua Jiang, Chufeng Nien, Shaun Stevens (2015)
Journal of the European Mathematical Society
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The Local Converse Problem is to determine how the family of the local gamma factors characterizes the isomorphism class of an irreducible admissible generic representation of , with a non-archimedean local field, where runs through all irreducible supercuspidal representations of and runs through positive integers. The Jacquet conjecture asserts that it is enough to take . Based on arguments in the work of Henniart and of Chen giving preliminary steps towards the Jacquet...
Nicolas Lerner (2006)
Bulletin de la Société Mathématique de France
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For a principal type pseudodifferential operator, we prove that condition implies local solvability with a loss of 3/2 derivatives. We use many elements of Dencker’s paper on the proof of the Nirenberg-Treves conjecture and we provide some improvements of the key energy estimates which allows us to cut the loss of derivatives from for any (Dencker’s most recent result) to 3/2 (the present paper). It is already known that condition doesimply local solvability with a loss of 1...
István Juhász, Jan van Mill (2018)
Commentationes Mathematicae Universitatis Carolinae
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We call a function P-preserving if, for every subspace with property P, its image also has property P. Of course, all continuous maps are both compactness- and connectedness-preserving and the natural question about when the converse of this holds, i.e. under what conditions such a map is continuous, has a long history. Our main result is that any nontrivial product function, i.e. one having at least two nonconstant factors, that has connected domain, range, and is connectedness-preserving...
Shahram Rezaei (2019)
Czechoslovak Mathematical Journal
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Let be a local ring, an ideal of and a nonzero Artinian -module of Noetherian dimension with . We determine the annihilator of the top local homology module . In fact, we prove that where denotes the smallest submodule of such that . As a consequence, it follows that for a complete local ring all associated primes of are minimal.