Local cohomological properties of homogeneous ANR compacta

V. Valov

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Displaying similar documents to “Local cohomological properties of homogeneous ANR compacta”

Movability and limits of polyhedra

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We define a metric $d_{S}$ , called the shape metric, on the hyperspace $2^{X}$ of all non-empty compact subsets of a metric space X. Using it we prove that a compactum X in the Hilbert cube is movable if and only if X is the limit of a sequence of polyhedra in the shape metric. This fact is applied to show that the hyperspace $(2^{ℝ} 2$ , dS) $i s s e p a r a b l e . O n t h e o t h e r h a n d, w e g i v e a n e x a m p l e s h o w i n g t h a t$ 2ℝ2 $i s n o t s e p a r a b l e i n t h e f u n d a m e n t a l m e t r i c i n t r o d u c e d b y B o r s u k .$

The compacta X in $S^{n}$ for which Sh(X) = Sh( $S^{k}$ ) is equivalent to $S^{n}$ -X ≈ $S^{n}$ - $S^{k}$

T. Rushing (1977)

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Notes on Retracts of Coset Spaces

J. van Mill, G. J. Ridderbos (2005)

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We study retracts of coset spaces. We prove that in certain spaces the set of points that are contained in a component of dimension less than or equal to n, is a closed set. Using our techniques we are able to provide new examples of homogeneous spaces that are not coset spaces. We provide an example of a compact homogeneous space which is not a coset space. We further provide an example of a compact metrizable space which is a retract of a homogeneous compact space, but which is not...

On a metrization of the hyperspace of a metric space

Karol Borsuk (1977)

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Naturally reductive homogeneous $(α, β)$ -metric spaces

M. Parhizkar, H.R. Salimi Moghaddam (2021)

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In the present paper we study naturally reductive homogeneous $(α, β)$ -metric spaces. We show that for homogeneous $(α, β)$ -metric spaces, under a mild condition, the two definitions of naturally reductive homogeneous Finsler space, given in the literature, are equivalent. Then, we compute the flag curvature of naturally reductive homogeneous $(α, β)$ -metric spaces.

n-movable compacta and ANR-systems

G. Kozlowski, Jack Segal (1974)

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Strong Cohomological Dimension

Jerzy Dydak, Akira Koyama (2008)

Bulletin of the Polish Academy of Sciences. Mathematics

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We characterize strong cohomological dimension of separable metric spaces in terms of extension of mappings. Using this characterization, we discuss the relation between strong cohomological dimension and (ordinal) cohomological dimension and give examples to clarify their gaps. We also show that $I n d_{G} X = d i m_{G} X$ if X is a separable metric ANR and G is a countable Abelian group. Hence $d i m_{ℤ} X = d i m X$ for any separable metric ANR X.

Some dimensional results for a class of special homogeneous Moran sets

Xiaomei Hu (2016)

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We construct a class of special homogeneous Moran sets, called ${m_{k}}$ -quasi homogeneous Cantor sets, and discuss their Hausdorff dimensions. By adjusting the value of ${m_{k}}_{k \geq 1}$ , we constructively prove the intermediate value theorem for the homogeneous Moran set. Moreover, we obtain a sufficient condition for the Hausdorff dimension of homogeneous Moran sets to assume the minimum value, which expands earlier works.

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Equivalence of the Borsuk and the ANR-system approach to shapes

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On decreasing sequences of compact absolute retracts

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