In this paper we introduce the category Apro-ANR called the approximate pro-category of ANRâ€™s, whose objects are all systems of ANRâ€™s and whose morphisms are obtained as equivalence classes of systemâ€¦ (More)

The notion of shape fibration between compact metric spaces was introduced by S. MardeÅ¡iÄ‡ and T. B. Rushing. MardeÅ¡iÄ‡ extended the notion to arbitrary topological spaces. A shape fibration f : X â†’ Yâ€¦ (More)

This paper concerns the shape theory for triads of spaces which was introduced by the author. More precisely, in the first part, the shape dimension for triads of spaces (X; X0,X1) is introduced, andâ€¦ (More)

Lisica and MardeÅ¡iÄ‡ introduced the notion of coherent expansion of a space to develop a strong shape theory for arbitrary topological spaces. MardeÅ¡iÄ‡ then introduced the notion of strongâ€¦ (More)

In this paper we develop the shape theory for triads of spaces in a systematic way, using polyhedral resolutions for triads of spaces, and give applications, which include the Blakers-Massey homotopyâ€¦ (More)

It is well-known that every continuous map is the composite of a homotopy equivalence and a fibration. In this paper, we introduce the notion of uniform shape fibration, and show that every uniformlyâ€¦ (More)

In the theory of inverse systems, in order to study the properties of a space X or a map f : X â†’ Y between spaces, one expands X to an inverse system X or expands f to a map f : X â†’ Y between theâ€¦ (More)