Fundamental dimensionality of compacts

Abstract

The paper is the investigation in the field of shape theory and is aimed at the consideration of fundamental dimensionality properties for compacts, being situated in a compact of the given topological dimensionality. The obtaining of the Gurevich's theorem analog about the dimensionality decrease with continuous mappings is also the aim of the paper. As a result a problem about fundamental dimensionalities of subcompacts has been solved. The Gurevich's theorem analog about the dimensionality decrease and estimation for fundamental dimensionalities of an image and pre-image with continuous mappings has been givenAvailable from VNTIC / VNTIC - Scientific & Technical Information Centre of RussiaSIGLERURussian Federatio