Open AccessCovariant Functors and Shapes in the Category of Compacts
Author(s) -
T. F. Zhuraev,
Z. O. Tursunova,
Kamariddin Rizokulovich Zhuvonov
Publication year - 2019
Publication title -
sovremennaâ matematika. fundamentalʹnye napravleniâ
Language(s) - English
Resource type - Journals
eISSN - 2949-0618
pISSN - 2413-3639
DOI - 10.22363/2413-3639-2019-65-1-21-32
Subject(s) - functor , covariant transformation , pure mathematics , mathematics , equivalence (formal languages) , linear subspace , space (punctuation) , compact space , derived category , action (physics) , algebra over a field , geometry , physics , computer science , operating system , quantum mechanics
In this paper, we consider covariant functors F : Comp → Comp acting in category of shape-preserving compact sets [2], innite compact sets, and shape equivalence [9]. Also we study action of compact functors and shape properties of the compact space X consisting of connected components ОX of the compact X as well as shape identity ShX = ShY of innite compacts X and Y for the space P (X) of probability measures and its subspaces.