Page 1 Next

Displaying 1 – 20 of 102

Showing per page

A dimension raising hereditary shape equivalence

Jan Dijkstra (1996)

Fundamenta Mathematicae

We construct a hereditary shape equivalence that raises transfinite inductive dimension from ω to ω+1. This shows that ind and Ind do not admit a geometric characterisation in the spirit of Alexandroff's Essential Mapping Theorem, answering a question asked by R. Pol.

All CAT(0) boundaries of a group of the form H × K are CE equivalent

Christopher Mooney (2009)

Fundamenta Mathematicae

M. Bestvina has shown that for any given torsion-free CAT(0) group G, all of its boundaries are shape equivalent. He then posed the question of whether they satisfy the stronger condition of being cell-like equivalent. In this article we prove that the answer is "Yes" in the situation where the group in question splits as a direct product with infinite factors. We accomplish this by proving an interesting theorem in shape theory.

Bimorphisms in pro-homotopy and proper homotopy

Jerzy Dydak, Francisco Ruiz del Portal (1999)

Fundamenta Mathematicae

A morphism of a category which is simultaneously an epimorphism and a monomorphism is called a bimorphism. The category is balanced if every bimorphism is an isomorphism. In the paper properties of bimorphisms of several categories are discussed (pro-homotopy, shape, proper homotopy) and the question of those categories being balanced is raised. Our most interesting result is that a bimorphism f:X → Y of t o w ( H 0 ) is an isomorphism if Y is movable. Recall that ( H 0 ) is the full subcategory of p r o - H 0 consisting of...

Classifying finite-sheeted covering mappings of paracompact spaces.

Vlasta Matijevic (2003)

Revista Matemática Complutense

The main result of the present paper is a classification theorem for finite-sheeted covering mappings over connected paracompact spaces. This theorem is a generalization of the classical classification theorem for covering mappings over a connected locally pathwise connected semi-locally 1-connected space in the finite-sheeted case. To achieve the result we use the classification theorem for overlay structures which was recently proved by S. Mardesic and V. Matijevic (Theorems 1 and 4 of [5]).

Currently displaying 1 – 20 of 102

Page 1 Next