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1
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Functional characterizations of p-spaces

100%
Holá Ľ.
Open Mathematics
|
2013
|
tom 11
|
nr 12
2197-2202
EN
We show that a completely regular space Y is a p-space (a Čech-complete space, a locally compact space) if and only if given a dense subspace A of any topological space X and a continuous f: A → Y there are a p-embedded subset (resp. a G δ-subset, an open subset) M of X containing A and a quasicontinuous subcontinuous extension f*: M → Y of f continuous at every point of A. A result concerning a continuous extension to a residual set is also given.
2
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On Asymmetric Distances

76%
Mennucci A. C. G.
Analysis and Geometry in Metric Spaces
|
2013
|
tom 1
200-231
EN
In this paper we discuss asymmetric length structures and asymmetric metric spaces. A length structure induces a (semi)distance function; by using the total variation formula, a (semi)distance function induces a length. In the first part we identify a topology in the set of paths that best describes when the above operations are idempotent. As a typical application, we consider the length of paths defined by a Finslerian functional in Calculus of Variations. In the second part we generalize the setting of General metric spaces of Busemann, and discuss the newly found aspects of the theory: we identify three interesting classes of paths, and compare them; we note that a geodesic segment (as defined by Busemann) is not necessarily continuous in our setting; hence we present three different notions of intrinsic metric space.
3
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Spectral Calculus and Lipschitz Extension for Barycentric Metric Spaces

76%
Mendel M., Naor A.
Analysis and Geometry in Metric Spaces
|
2013
|
tom 1
163-199
EN
The metric Markov cotype of barycentric metric spaces is computed, yielding the first class of metric spaces that are not Banach spaces for which this bi-Lipschitz invariant is understood. It is shown that this leads to new nonlinear spectral calculus inequalities, as well as a unified framework for Lipschitz extension, including new Lipschitz extension results for CAT (0) targets. An example that elucidates the relation between metric Markov cotype and Rademacher cotype is analyzed, showing that a classical Lipschitz extension theorem of Johnson, Lindenstrauss and Benyamini is asymptotically sharp.
4
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Functor of extension in Hilbert cube and Hilbert space

76%
Niemiec P.
Open Mathematics
|
2014
|
tom 12
|
nr 6
887-895
EN
It is shown that if Ω = Q or Ω = ℓ 2, then there exists a functor of extension of maps between Z-sets in Ω to mappings of Ω into itself. This functor transforms homeomorphisms into homeomorphisms, thus giving a functorial setting to a well-known theorem of Anderson [Anderson R.D., On topological infinite deficiency, Michigan Math. J., 1967, 14, 365–383]. It also preserves convergence of sequences of mappings, both pointwise and uniform on compact sets, and supremum distances as well as uniform continuity, Lipschitz property, nonexpansiveness of maps in appropriate metrics.
5
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The homotopies of admissible multivalued mappings

76%
Ślosarski M.
Open Mathematics
|
2012
|
tom 10
|
nr 6
2187-2199
EN
Certain properties of homotopies of admissible multivalued mappings shall be presented, along with their applications as the tool for examining the acyclicity of a space.
6
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On minimal Hausdorff and minimal Urysohn functions

64%
Cammaroto F., Catalioto A., Porter J.
Open Mathematics
|
2011
|
tom 9
|
nr 6
1242-1251
EN
In this article, we extend the work on minimal Hausdorff functions initiated by Cammaroto, Fedorchuk and Porter in a 1998 paper. Also, minimal Urysohn functions are introduced and developed. The properties of heredity and productivity are examined and developed for both minimal Hausdorff and minimal Urysohn functions.
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