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]).
Coherent and strong expansions of spaces coincide
In the existing literature there are several constructions of the strong shape category of topological spaces. In the one due to Yu. T. Lisitsa and S. Mardešić [LM1-3] an essential role is played by coherent polyhedral (ANR) expansions of spaces. Such expansions always exist, because every space admits a polyhedral resolution, resolutions are strong expansions and strong expansions are always coherent. The purpose of this paper is to prove that conversely, every coherent polyhedral (ANR) expansion...
Concordance of compacta
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.
Distributeurs et théorie de la forme
Enriched orthogonality and equivalences.
Equivalence of the Borsuk and the ANR-system approach to shapes
Equivariant shape
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)...
Generalized paths and pointed 1-movability
Homeomorphic neighborhoods in -manifolds