Covariant Functors and Shapes in the Category of Compacts
T. F. ZhuraevTashkent State Pedagogical University named after NizamiЗ. О. ТурсуноваTashkent State Pedagogical University named after NizamiKamariddin Rizokulovich ZhuvonovTashkent State Pedagogical University named after Nizami
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In this paper, we consider covariant functors F : Comp → Comp acting in category of shape-preserving compact sets [2], infinite 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 infinite compacts X and Y for the space P (X) of probability measures and its subspaces.
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