Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Locallyn-Connected Compacta and UV n -Maps

100%

Valov V.

Analysis and Geometry in Metric Spaces

2015

tom 3

nr 1

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.

Local cohomological properties of homogeneous ANR compacta

100%

Valov V.

Fundamenta Mathematicae

2016

tom 233

nr 3

257-270

In accordance with the Bing-Borsuk conjecture, we show that if X is an n-dimensional homogeneous metric ANR continuum and x ∈ X, then there is a local basis at x consisting of connected open sets U such that the cohomological properties of Ū and bd U are similar to the properties of the closed ball 𝔹ⁿ ⊂ ℝⁿ and its boundary $𝕊^{n-1}$. We also prove that a metric ANR compactum X of dimension n is dimensionally full-valued if and only if the group Hₙ(X,X∖x;ℤ) is not trivial for some x ∈ X. This implies that every 3-dimensional homogeneous metric ANR compactum is dimensionally full-valued.

Ograniczanie wyników

1 Analysis and Geometry in Metric Spaces

1 Fundamenta Mathematicae

2 Valov V.

1 2016

1 2015

Wyniki wyszukiwania

Locallyn-Connected Compacta and UV n -Maps

Local cohomological properties of homogeneous ANR compacta