Weakly infinite-dimensional spaces

Fedorchuk, V. V.

doi:10.1070/rm2007v062n02abeh004397

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Introduction4

Question 1 Is the Dimension Scale Of Every Metrizable C-com1

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Cited by 10 publications

(5 citation statements)

References 66 publications

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“…The results of this paper not concerning cohomological dimension were announced in [5]. All spaces are assumed normal, and all mappings are assumed continuous.…”

Section: Question 1 Is the Dimension Scale Of Every Metrizable C-commentioning

confidence: 99%

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Dimension scales of bicompacta

Fedorchuk

2008

Sib Math J

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“…The results of this paper not concerning cohomological dimension were announced in [5]. All spaces are assumed normal, and all mappings are assumed continuous.…”

Section: Question 1 Is the Dimension Scale Of Every Metrizable C-commentioning

confidence: 99%

“…Concerning the transfinite Borst dimensions [4] and their modifications [5], we just note that there is a metrizable compactum X that has dimension dim 2 X = α < ω 1 , but lacks any compactum Y of finite positive dimension dim 2 Y = dim Y (see [5,Appendix]). …”

Section: Introductionmentioning

confidence: 99%

Dimension scales of bicompacta

Fedorchuk

2008

Sib Math J

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“…It should be remarked that a C-space X is paracompact if and only if it is countably paracompact and normal, see e.g. [6,Proposition 1.3]. Every finite-dimensional paracompact space, as well as every countable-dimensional metrizable space, is a C-space [1], but there exists a compact metric C-space which is not countabledimensional [14].…”

Section: Introductionmentioning

confidence: 99%

Constructing selections stepwise over cones of simplicial complexes

Gutev

2020

Topology and its Applications

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It is obtained a natural generalisation of Uspenskij's selection characterisation of paracompact C-spaces. The method developed to achieve this result is also applied to give a simplified proof of a similar characterisation of paracompact finite C-space obtained previously by Valov. Another application is a characterisation of finite-dimensional paracompact spaces which generalises both a remark done by Michael and a result obtained by the author.

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“…It should be remarked that a C-space is paracompact if and only if it is countably paracompact and normal, see e.g. [6,Proposition 1.3]. Every finitedimensional paracompact space, as well as every countable-dimensional metrizable space, is a C-space [1], but there exists a compact metric C-space which is not countable-dimensional [17].…”

Section: Introductionmentioning

confidence: 99%

Near-selection theorems for C-spaces

Gutev¹

2019

Preprint

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Haver's near-selection theorem deals with approximate selections of Hausdorff continuous CE-valued mappings defined on σ-compact metrizable C-spaces. In the present paper, we extend this theorem to all paracompact C-spaces. The technique developed to achieve this generalisation is based on oriented simplicial complexes. This approach makes not only a considerable simplification in the proof but is also successful in generalising the special case of compact metric C-spaces to all paracompact finite C-spaces.

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Weakly infinite-dimensional spaces

Cited by 10 publications

References 66 publications

Dimension scales of bicompacta

Dimension scales of bicompacta

Constructing selections stepwise over cones of simplicial complexes

Near-selection theorems for C-spaces

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