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
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