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1
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The ANR-property of hyperspaces with the Attouch-Wets topology

100%
Voytsitskyy R.
Open Mathematics
|
2008
|
tom 6
|
nr 2
228-236
EN
We characterize metric spaces whose hyperspaces of non-empty closed, bounded, compact or finite subsets, endowed with the Attouch-Wets topology, are absolute (neighborhood) retracts.
2
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Locallyn-Connected Compacta and UV n -Maps

64%
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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Spaces of measurable functions

64%
Niemiec P.
Open Mathematics
|
2013
|
tom 11
|
nr 7
1304-1316
EN
For a metrizable space X and a finite measure space (Ω, $\mathfrak{M}$, µ), the space M µ(X) of all equivalence classes (under the relation of equality almost everywhere mod µ) of $\mathfrak{M}$-measurable functions from Ω to X, whose images are separable, equipped with the topology of convergence in measure, and some of its subspaces are studied. In particular, it is shown that M µ(X) is homeomorphic to a Hilbert space provided µ is (nonzero) nonatomic and X is completely metrizable and has more than one point.
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