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On H ˇ n -bubbles in n-dimensional compacta

Umed Karimov, Dušan Repovš (1998)

Colloquium Mathematicae

A topological space X is called an H ˇ n -bubble (n is a natural number, H ˇ n is Čech cohomology with integer coefficients) if its n-dimensional cohomology H ˇ n ( X ) is nontrivial and the n-dimensional cohomology of every proper subspace is trivial. The main results of our paper are: (1) Any compact metrizable H ˇ n -bubble is locally connected; (2) There exists a 2-dimensional 2-acyclic compact metrizable ANR which does not contain any H ˇ 2 -bubbles; and (3) Every n-acyclic finite-dimensional L H ˇ n -trivial metrizable compactum...

On the disjoint (0,N)-cells property for homogeneous ANR's

Paweł Krupski (1993)

Colloquium Mathematicae

A metric space (X,ϱ) satisfies the disjoint (0,n)-cells property provided for each point x ∈ X, any map f of the n-cell B n into X and for each ε > 0 there exist a point y ∈ X and a map g : B n X such that ϱ(x,y) < ε, ϱ ^ ( f , g ) < ε and y g ( B n ) . It is proved that each homogeneous locally compact ANR of dimension >2 has the disjoint (0,2)-cells property. If dimX = n > 0, X has the disjoint (0,n-1)-cells property and X is a locally compact L C n - 1 -space then local homologies satisfy H k ( X , X - x ) = 0 for k < n and Hn(X,X-x) ≠ 0.

Some topics concerning homeomorphic parameterizations.

Stephen Semmes (2001)

Publicacions Matemàtiques

In this survey, we consider several questions pertaining to homeomorphisms, including criteria for their existence in certain circumstances, and obstructions to their existence.

The cell-like approximation theorem in dimension 5

Robert J. Daverman, Denise M. Halverson (2007)

Fundamenta Mathematicae

The cell-like approximation theorem of R. D. Edwards characterizes the n-manifolds precisely as the resolvable ENR homology n-manifolds with the disjoint disks property for 5 ≤ n < ∞. Since no proof for the n = 5 case has ever been published, we provide the missing details about the proof of the cell-like approximation theorem in dimension 5.

The generalized Schoenflies theorem for absolute suspensions

David P. Bellamy, Janusz M. Lysko (2005)

Colloquium Mathematicae

The aim of this paper is to prove the generalized Schoenflies theorem for the class of absolute suspensions. The question whether the finite-dimensional absolute suspensions are homeomorphic to spheres remains open. Partial solution to this question was obtained in [Sz] and [Mi]. Morton Brown gave in [Br] an ingenious proof of the generalized Schoenflies theorem. Careful analysis of his proof reveals that modulo some technical adjustments a similar argument gives an analogous result for the class...

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