TWO APPROACHES TO PROPER SHAPE THEORY

Abstract

The first proper shape category is constructed in [1] by embedding a separable locally compact metric space in Hilbert cube without a point and by considering classes of proper fundamental nets as morphisms. In this paper we give a direct proof that this category is a subcategory of the proper shape category obtained by inverse systems of ANR’s and proper maps. At the end are shown the main properties of the proper shape theory by use of inverse systems.