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Józef Chaber 《Topology and its Applications》1982,14(2):131-142
We investigate the classes of spaces that can be mapped onto a metrizable space by a closed mapping with fibers having a given property . We give some conditions which assure that such classes are closed under the action of perfect or open and compact mappings. Such a treatment includes the investigation of paracompact p-spaces and M-spaces. We also discuss spaces that can be mapped onto a metacompact Moore space. 相似文献
2.
A Borel derivative on the hyperspace 2
X
of a compactumX is a Borel monotone mapD: 2
X
→2
X
. The derivative determines a Cantor-Bendixson type rank δ:2X → ω1 ∪ {∞} . We show that ifA⊂2
X
is analytic andZ⊂A intersects stationary many layers δ−1({ξ}), then for almost all σ,F∩δ−1({ξ}) cannot be separated fromZ ∩∪
a<ξ
δ−1({a}) (and also fromZ ∩∪
a>ξ
δ−1({a}) by anyF
σ-set. Another main result involves a natural partial order on 2
X
related to the derivative. The results are obtained in a general framework of “resolvable ranks” introduced in the paper.
During our work on this paper the second author was a Visiting Professor at the Miami University, Ohio. This author would
like to express his gratitude to the Department of Mathematics and Statistics for the hospitality. 相似文献
3.
J. Chaber 《Topology and its Applications》1982,14(1):31-41
We give characterizations of perfect images and open and compact images of spaces that can be mapped onto metrizable spaces by a mapping with fibers having a given property . We use these characterizations to obtain conditions which imply that such images can be mapped onto a metric space by a mapping with fibers satisfying . Such a treatment includes the investigation of spaces with a weaker metric topology [2, Ch. 5]. 相似文献
4.
Nonlinear Dynamics - This paper considers the problem of pruning recurrent neural models of perceptron type with one hidden layer which may be used for modelling of dynamic system. In order to... 相似文献
5.
Józef Chaber 《Topology and its Applications》1982,14(3):241-246
We give a characterization of open finite-to-one images of metric spaces and apply this characterization in the investigation of open finite-to-one images of paracompact p-spaces. 相似文献
6.
Nebeluk Robert Zarzycki Krzysztof Seredyński Dawid Chaber Patryk Figat Maksym Domański Paweł D. Zieliński Cezary 《Nonlinear dynamics》2023,111(9):8383-8395
Nonlinear Dynamics - Moving-object tracking using a pan–tilt camera setup is quite a well-known task in robotics. However, the presented research addresses specific properties of the tracked... 相似文献
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