Tameness and Movability in Proper Shape Theory
by
Zvonko Čerin
University of Zagreb
Coauthors: Gian Mario Gianella (Universitá di Torino)

The notions and results in this paper belong to the part of topology that could be described as proper shape theory. As shape theory is an improved homotopy theory designed to handle more successfully complicated spaces so is proper shape theory a modification of proper homotopy theory made with the same goal to provide us with a new insight into global properties even of those spaces for which the classical proper homotopy gives doubtful information.

The first author has described proper shape category of all topological spaces using Sanjurjo's method of multi-valued functions. This approach is formally very similar to the one taken by Ball and Sher. Instead of proper fundamental nets we considered proper multi-nets. The other steps are identical. We defined a notion of a proper homotopy for proper multi-nets and take for the morphisms of the proper shape category proper homotopy classes of proper multi-nets.

In this paper we shall study properly M^B_C tame and properly M^B movable spaces, where B and C denote classes of topological spaces. Both proper tameness and proper movability are invariants of proper shape theory and are described by the use of proper multi-valued functions. The first is analogous to L. Siebenmann's notion of a tame at infinity space while the second is modelled on Borsuk's concept of movability in shape theory.

Date received: April 12, 1996

Copyright © 1996 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caae-13.