Results 21 to 30 of about 242 (55)

Preservation of the Borel class under open-$LC$ functions

, 2011
Let $X$ be a Borel subset of the Cantor set \textbf{C} of additive or multiplicative class ${\alpha},$ and $f: X \to Y$ be a continuous function with compact preimages of points onto $Y \subset \textbf{C}.$ If the image $f(U)$ of every clopen set $U$ is ...
Ostrovsky, Alexey
core   +1 more source

Lipschitz retraction of finite subsets of Hilbert spaces

, 2015
Finite subset spaces of a metric space $X$ form a nested sequence under natural isometric embeddings $X=X(1)\subset X(2)\subset\dots$. We prove that this sequence admits Lipschitz retractions $X(n)\to X(n-1)$ when $X$ is a Hilbert space.Comment ...
Kovalev, Leonid V.
core   +1 more source

Maps preserving absolute continuity and singularity of positive operators [PDF]

, 2020
In this paper we consider the cone of all positive, bounded operators acting on an infinite dimensional, complex Hilbert space, and examine bijective maps that preserve absolute continuity in both directions.
Gehér, György, Tarcsay, Zsigmond, Titkos, Tamás   +2 more
core   +2 more sources

Echeloned Spaces

Forum of Mathematics, Sigma
We introduce the notion of echeloned spaces – an order-theoretic abstraction of metric spaces. The first step is to characterize metrizable echeloned spaces. It turns out that morphisms between metrizable echeloned spaces are uniformly continuous or have
Maxime Gheysens, Bojana Pavlica, Christian Pech, Maja Pech, Friedrich Martin Schneider   +4 more
doaj   +1 more source

Nonexistence of linear operators extending Lipschitz (pseudo)metric

, 2012
We present an example of a zero-dimensional compact metric space $X$ and its closed subspace $A$ such that there is no continuous linear extension operator for the Lipschitz pseudometrics on $A$ to the Lipschitz pseudometrics on $X$.
Repovš, Dušan, Zarichnyi, Mykhailo
core   +1 more source

ℐ-sn-metrizable spaces and the images of semi-metric spaces

Open Mathematics
The theory of generalized metric spaces is an active topic in general topology. In this article, we utilize the concepts of ideal convergence and networks to discuss the metrization problem and the mutual classification problem between spaces and ...
Zhou Xiangeng, Liu Fang, Liu Li, Lin Shou   +3 more
doaj   +1 more source

On Lipschitz Retraction of Finite Subsets of Normed Spaces

, 2019
If $X$ is a metric space, then its finite subset spaces $X(n)$ form a nested sequence under natural isometric embeddings $X = X(1)\subset X(2) \subset \cdots$.
Akofor, Earnest
core   +1 more source

On mapping properties and the property of Kelley [PDF]

, 2002
Mapping conditions are studied under which a continuum having the property of Kelley has this property hereditarily.
J. J. Charatonik
core   +1 more source

Existence and convergence of fixed points for mappings of asymptotically nonexpansive type in uniformly convex W-hyperbolic spaces

Fixed Point Theory and Applications, 2011
Uniformly convex W-hyperbolic spaces with monotone modulus of uniform convexity are a natural generalization of both uniformly convexnormed spaces and CAT(0) spaces.
Cui Yunan, Zhang Jingxin
doaj  

Lattictic non-archimedean random stability of ACQ functional equation

Advances in Difference Equations, 2011
In this paper, we prove the generalized Hyers-Ulam stability of the following additive-cubic-quartic functional equation 1 1 f ( x + 2 y ) + 1 1 f ( x - 2 y ) = 4 4 f ( x + y ) + 4 4 f ( x - y ) + 1 2 f ( 3 y ) - 4 8 f ( 2 ...
Saadati Reza, Cho Yeol
doaj