Locallyn-Connected Compacta and UV ⁿ-Maps

• Autorzy: V. Valov
• Języki publikacji: EN

Abstrakty

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.

Słowa kluczowe

EN

absolute neighborhood retracts; ALCn-spaces; cell-like maps and spaces; WLCn-spaces; UVn-maps and space

Kategorie tematyczne

• 54E35: Metric spaces, metrizability
• 54C55: Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties)
• 54D05: Connected and locally connected spaces (general aspects)
• 54E40: Special maps on metric spaces

• Wydawca: De Gruyter Open
• Czasopismo: Analysis and Geometry in Metric Spaces
• Rocznik: 2015
• Tom: 3
• Numer: 1

Daty

otrzymano

2015-01-02

zaakceptowano

2015-04-10

online

2015-04-29

Twórcy

autor

V. Valov

• Department of Computer Science and Mathematics, Nipissing University, 100 College Drive, P.O. Box 5002, North Bay, ON, P1B 8L7, Canada

Bibliografia

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Identyfikatory

DOI

10.1515/agms-2015-0006