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