A suspension theorem for the proper homotopy and strong shape theories
A Whitehead theorem in CG-shape
Algebraic topology for proper shape theory
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]).
Fundamental pro-groupoids and covering projections
We introduce a new notion of covering projection E → X of a topological space X which reduces to the usual notion if X is locally connected. We use locally constant presheaves and covering reduced sieves to find a pro-groupoid π crs (X) and an induced category pro (π crs (X), Sets) such that for any topological space X the category of covering projections and transformations of X is equivalent to the category pro (π crs (X), Sets). We also prove that the latter category is equivalent to pro (π CX,...
Generalized universal covering spaces and the shape group
If a paracompact Hausdorff space X admits a (classical) universal covering space, then the natural homomorphism φ: π₁(X) → π̌₁(X) from the fundamental group to its first shape homotopy group is an isomorphism. We present a partial converse to this result: a path-connected topological space X admits a generalized universal covering space if φ: π₁(X) → π̌₁(X) is injective. This generalized notion of universal covering p: X̃ → X enjoys most of the usual properties, with the possible exception of evenly...
On approximate n-connectedness
On shape groups and Cech homology groups of a compact space
On the shape of pointed compact connected subsets of
Shape evaluation groups
The fundamental groups of subsets of closed surfaces inject into their first shape groups.
The Hurewicz and Whitehead theorems with compact carriers