Shape theory is a new and important branch of geometric topology. Its rapid development is
due to the fact that it affords a natural way to deal with homotopy properties of general …

This expository article on Shape Theory contains the main concepts of this theory with a
formulation of the most important results of this theory and also with some open problems …

1. Introduction. A. What is a finiteness theorem! Suppose that ƒ is a mapping from some
closed manifold M onto another, say N. We shall be interested in placing local assumptions …

Abstract, Let F:(X, x)-+(Y, y) be a shape morphism with (X, x) and (Г, y) pointed movable
metric continua of finite dimension. A theorem of M. Moszynska asserts that if F,: nk {X, x …

Abstract Let f: S 3→ S 2 be a continuous function. If yϵS 2 assume that f-1 (y) has the shape
of a circle and that there are neighborhoods V⊂ U of f-1 (y) such that for any point inverse f …

Sažetak The paper outlines the development of shape theory since its founding by K. Borsuk
30 years ago to the present days. As a motivation for introducing shape theory, some …

A Vietoris–Begle theorem for connective Steenrod homology theories and cell-like maps
between metric compacta - ScienceDirect Skip to main contentSkip to article Elsevier logo …

Nunnerous mathematicians have proved theorems of Hurewicz type in different contexts
shape theory, pro-categories, coherent categories. In this paper we obtain a Hurewicz …

Sažetak Let (X, A, x) be an n-connected inverse system of CW-pairs such that the restriction
(A, x) is m-connected. We prove that there exists an isomorphic inverse system (Y, B, y) …

Our approach enables us to define the k-th homotopy pro-group ark {(X, x0)} of a pointed
topological space (X, x0). The homotopy progroups play the central role in the Whitehead …