A counterexample concerning products in the shape category
We exhibit a metric continuum X and a polyhedron P such that the Cartesian product X × P fails to be the product of X and P in the shape category of topological spaces.
A dimension raising hereditary shape equivalence
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.
A note on the theory of shape of compacta
A suspension theorem for the proper homotopy and strong shape theories
A Whitehead theorem in CG-shape
Algebraic theory of fundamental dimension [Book]
All CAT(0) boundaries of a group of the form H × K are CE equivalent
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.
An intrinsic characterization of the shape of paracompacta by means of non-continuous single-valued maps.
An introduction to shape theory for the nonspecialist
An R-stable ANR which is not FR-stable
Approximate polyhedra, resolutions of maps and shape fibrations
Bimorphisms in pro-homotopy and proper homotopy
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 is an isomorphism if Y is movable. Recall that is the full subcategory of consisting of...
-Movably regular convergences
Čech methods and the adjoint functor theorem
Chapman's category isomorphism for arbitrary ARs
Classifying finite-sheeted covering mappings of paracompact spaces.
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]).
Constructing exotic retracts, factors of manifolds, and generalized manifolds via decompositions
Coshape-invariant functors and Mackey's induced representation theorem
Counting shape and homotopy types among fundamental absolute neighborhood retracts: an elementary approach.
Cp-movable at infinity spaces, compact ANR divisors and property UVWn.