Fake topological Hilbert spaces and characterizations of dimension in terms of negligibility
Fiberwise shape theory.
Fibres of Hurewicz and approximate fibrations.
Finite-dimensional categorial complement theorems in shape theory
Finite-dimensional categorical complement theorems in strong shape theory and a principle of reversing maps between open subsets of spheres
Finite-dimensional complement theorems in shape theory and their relation to S-duality
Function spaces and shape theories
The purpose of this paper is to provide a geometric explanation of strong shape theory and to give a fairly simple way of introducing the strong shape category formally. Generally speaking, it is useful to introduce a shape theory as a localization at some class of “equivalences”. We follow this principle and we extend the standard shape category Sh(HoTop) to Sh(pro-HoTop) by localizing pro-HoTop at shape equivalences. Similarly, we extend the strong shape category of Edwards-Hastings to sSh(pro-Top)...