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Kolmogorov-Smirnov isometries and affine automorphisms of spaces of distribution functions

100%
Molnár L.
Open Mathematics
|
2011
|
tom 9
|
nr 4
789-796
EN
In this paper we describe the structure of surjective isometries of the spaces of all absolutely continuous, singular, or discrete probability distribution functions on R equipped with the Kolmogorov-Smirnov metric. We also study the structure of affine automorphisms of the space of all distribution functions.
2
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Locallyn-Connected Compacta and UV n -Maps

84%
Valov V.
Analysis and Geometry in Metric Spaces
|
2015
|
tom 3
|
nr 1
EN
We provide a machinery for transferring some properties of metrizable ANR-spaces to metrizable LCn-spaces. As a result, we show that for completely metrizable spaces the properties ALCn, LCn and WLCn coincide to each other. We also provide the following spectral characterizations of ALCn and celllike compacta: A compactum X is ALCn if and only if X is the limit space of a σ-complete inverse system S = {Xα , pβ α , α < β < τ} consisting of compact metrizable LCn-spaces Xα such that all bonding projections pβα, as a well all limit projections pα, are UVn-maps. A compactum X is a cell-like (resp., UVn) space if and only if X is the limit space of a σ-complete inverse system consisting of cell-like (resp., UVn) metrizable compacta.
3
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Isometry groups of non standard metric products

84%
Oliynyk B.
Open Mathematics
|
2013
|
tom 11
|
nr 2
264-273
EN
We consider isometry groups of a fairly general class of non standard products of metric spaces. We present sufficient conditions under which the isometry group of a non standard product of metric spaces splits as a permutation group into direct or wreath product of isometry groups of some metric spaces.
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