Displaying similar documents to “Attouch-Wets convergence and Kuratowski convergence on compact sets”

Function space topologies deriving from hypertopologies and networks

A. Di Concilio, A. Miranda (2001)

Bollettino dell'Unione Matematica Italiana

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In un progetto di generalizzazione delle classiche topologie di tipo «set-open» di Arens-Dugundji introduciamo un metodo generale per produrre topologie in spazi di funzioni mediante l'uso di ipertopologie. Siano X , Y spazi topologici e C X , Y l'insieme delle funzioni continue da X verso Y . Fissato un «network» α nel dominio X ed una topologia τ nell'iperspazio C L Y del codominio Y si genera una topologia τ α in C X , Y richiedendo che una rete f λ di C X , Y converge in τ α ad f C X , Y se e solo se la rete f λ A ¯ converge...

A generalization of boundedly compact metric spaces

Gerald Beer, Anna Di Concilio (1991)

Commentationes Mathematicae Universitatis Carolinae

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A metric space X , d is called a UC space provided each continuous function on X 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 UC spaces play relative to the compact metric spaces.

Generalizations to monotonicity for uniform convergence of double sine integrals over ℝ̅²₊

Péter Kórus, Ferenc Móricz (2010)

Studia Mathematica

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We investigate the convergence behavior of the family of double sine integrals of the form 0 0 f ( x , y ) s i n u x s i n v y d x d y , where (u,v) ∈ ℝ²₊:= ℝ₊ × ℝ₊, ℝ₊:= (0,∞), and f: ℝ²₊ → ℂ is a locally absolutely continuous function satisfying certain generalized monotonicity conditions. We give sufficient conditions for the uniform convergence of the remainder integrals a b a b to zero in (u,v) ∈ ℝ²₊ as maxa₁,a₂ → ∞ and b j > a j 0 , j = 1,2 (called uniform convergence in the regular sense). This implies the uniform convergence of the partial...

Properties of one-point completions of a noncompact metrizable space

Melvin Henriksen, Ludvík Janoš, Grant R. Woods (2005)

Commentationes Mathematicae Universitatis Carolinae

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If a metrizable space X is dense in a metrizable space Y , then Y is called a of X . If T 1 and T 2 are metric extensions of X and there is a continuous map of T 2 into T 1 keeping X pointwise fixed, we write T 1 T 2 . If X is noncompact and metrizable, then ( ( X ) , ) denotes the set of metric extensions of X , where T 1 and T 2 are identified if T 1 T 2 and T 2 T 1 , i.e., if there is a homeomorphism of T 1 onto T 2 keeping X pointwise fixed. ( ( X ) , ) is a large complicated poset studied extensively by V. Bel’nov [, Trans. Moscow Math....

Characterizing metric spaces whose hyperspaces are homeomorphic to ℓ₂

T. Banakh, R. Voytsitskyy (2008)

Colloquium Mathematicae

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It is shown that the hyperspace C l d H ( X ) (resp. B d d H ( X ) ) 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.

The AR-Property of the spaces of closed convex sets

Katsuro Sakai, Masato Yaguchi (2006)

Colloquium Mathematicae

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Let C o n v H ( X ) , C o n v A W ( X ) and C o n v W ( X ) be the spaces of all non-empty closed convex sets in a normed linear space X admitting the Hausdorff metric topology, the Attouch-Wets topology and the Wijsman topology, respectively. We show that every component of C o n v H ( X ) and the space C o n v A W ( X ) are AR. In case X is separable, C o n v W ( X ) is locally path-connected.

The order topology for a von Neumann algebra

Emmanuel Chetcuti, Jan Hamhalter, Hans Weber (2015)

Studia Mathematica

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The order topology τ o ( P ) (resp. the sequential order topology τ o s ( P ) ) on a poset P is the topology that has as its closed sets those that contain the order limits of all their order convergent nets (resp. sequences). For a von Neumann algebra M we consider the following three posets: the self-adjoint part M s a , the self-adjoint part of the unit ball M ¹ s a , and the projection lattice P(M). We study the order topology (and the corresponding sequential variant) on these posets, compare the order topology...

Pointwise convergence of nonconventional averages

I. Assani (2005)

Colloquium Mathematicae

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We answer a question of H. Furstenberg on the pointwise convergence of the averages 1 / N n = 1 N U ( f · R ( g ) ) , where U and R are positive operators. We also study the pointwise convergence of the averages 1 / N n = 1 N f ( S x ) g ( R x ) when T and S are measure preserving transformations.