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Displaying similar documents to “ A -compactifications and A -weight of Alexandroff spaces”

Note on the Wijsman hyperspaces of completely metrizable spaces

J. Chaber, R. Pol (2002)

Bollettino dell'Unione Matematica Italiana

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We consider the hyperspace C L X of nonempty closed subsets of completely metrizable space X endowed with the Wijsman topologies τ W d . If X is separable and d , e are two metrics generating the topology of X , every countable set closed in C L X , τ W e has isolated points in C L X , τ W d . For d = e , this implies a theorem of Costantini on topological completeness of C L X , τ W d . We show that for nonseparable X the hyperspace C L X , τ W d may contain a closed copy of the rationals. This answers a question of Zsilinszky.

Partial Hölder continuity results for solutions of non linear non variational elliptic systems with limit controlled growth

Luisa Fattorusso, Giovanna Idone (2002)

Bollettino dell'Unione Matematica Italiana

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Let Ω be a bounded open subset of R n , n > 4 , of class C 2 . Let u H 2 Ω a solution of elliptic non linear non variational system a x , u , D u , H u = b x , u , D u where a x , u , μ , ξ and b x , u , μ are vectors in R N , N 1 , measurable in x , continuous in u , μ , ξ and u , μ respectively. Here, we demonstrate that if b x , u , μ has limit controlled growth, if a x , u , μ , ξ is of class C 1 in ξ and satisfies the Campanato condition A and, together with a ξ , certain continuity assumptions, then the vector D u is partially Hölder continuous for every exponent α < 1 - n p .

Homogenization of some nonlinear problems with specific dependence upon coordinates

P. Courilleau, S. Fabre, J. Mossino (2001)

Bollettino dell'Unione Matematica Italiana

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Questo articolo considera una successione di equazioni differenziali a derivate parziali non lineari in forma di divergenza del tipo - div Q ϵ G x , N ϵ u = f ϵ , in un dominio limitato Ω dello spazio n -dimensionale; Q ϵ = Q ϵ x e N ϵ = N ϵ x sono matrici con coefficenti limitati, N ϵ e è invertibile e la sua matrice inversa R ϵ ha anche coefficenti limitati. La non linearità è dovuta alla funzione G = G x , ξ ; la condizione di crescita, la monotonicità e le ipotesi di coercitività sono modellate sul p -Laplaciano, 1 < p < , ed assicurano l'esistenza di...

Some Separation Axioms Via Ideals

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 T 2 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....

The Schreier Property and Gauss' Lemma

Daniel D. Anderson, Muhammad Zafrullah (2007)

Bollettino dell'Unione Matematica Italiana

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Let D be an integral domain with quotient field D . Recall that D is Schreier if D is integrally closed and for all x , y , z D { 0 } , x | y z implies that x = r s where r | y e s | z . A GCD domain is Schreier. We show that an integral domain D is a GCD domain if and only if (i) for each pair a , b D { 0 } , there is a finitely generated ideal B such that a D b D = B v and (ii) every quadratic in D [ X ] that is a product of two linear polynomials in K [ X ] is a product of two linear polynomials in D [ X ] . We also show that D is Schreier if and only if every...

Remarks on 𝒮 -Closedness in Topological Spaces

Zbigniew Duszyński (2007)

Bollettino dell'Unione Matematica Italiana

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Corresponding to [27], some properties of S-closed subspaces and subsets 𝒮 -closed relative to a topological space are proved. Conditions under which mappings preserve certain 𝒮 -closed subspaces are investigated.

On nowhere first-countable compact spaces with countable π -weight

Jan van Mill (2015)

Commentationes Mathematicae Universitatis Carolinae

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The minimum weight of a nowhere first-countable compact space of countable π -weight is shown to be κ B , the least cardinal κ for which the real line can be covered by κ many nowhere dense sets.

Eisenstein ideal and reducible λ -adic Representations Unramified Outside a Finite Number of Primes.

Miriam Ciavarella (2006)

Bollettino dell'Unione Matematica Italiana

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The object of this note is to study certain 2-dimensional λ -adic representations of Gal ( Q ¯ / Q ) ; fixed p 1 , , p n distinct primes, we will consider representations ρ : G G L 2 ( A ) , given by the matrix ρ = ( a b c d ) which are unramified outside p 1 , , p n , and the residue characteristic of λ , which are a product of m representations over finite extensions of the ring of Witt vectors of the residue field and which are reducible modulo λ . In analogy with the theory of the modular representations, we will introduce the analogue of Mazur's Hecke...