International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 2, Pages 291-298
doi:10.1155/S0161171296000403

Proper shape invariants: Tameness and movability

Abstract

We study geometric properties of topological spaces called proper NCℬ-tameness, proper PCℬ-tameness, and proper Nℬ-movability, where ℬ and C denote classes of spaces. They are related to proper MCℬ-tameness and proper Mℬ-movability from [5] and could be regarded as their dual forms. All three are invariants of a recently invented author's proper shape theory and are described by the use of proper multi-valued functions. We explore their basic properties and prove several results on their preservation under proper maps.