Covariant Functors and Shapes in the Category of Compacts
- Authors: Zhuraev TF1, Tursunova ZO1, Zhuvonov KR1
-
Affiliations:
- Tashkent State Pedagogical University named after Nizami
- Issue: Vol 65, No 1 (2019): Contemporary Problems in Mathematics and Physics
- Pages: 21-32
- Section: New Results
- URL: https://journals.rudn.ru/CMFD/article/view/22238
- DOI: https://doi.org/10.22363/2413-3639-2019-65-1-21-32
Cite item
Full Text
Abstract
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.
About the authors
T F Zhuraev
Tashkent State Pedagogical University named after Nizami
Email: tursunzhuraev@mail.ru
Tashkent, Uzbekistan
Z O Tursunova
Tashkent State Pedagogical University named after Nizami
Email: zulayhotursunova@mail.ru
Tashkent, Uzbekistan
K R Zhuvonov
Tashkent State Pedagogical University named after Nizami
Email: qamariddin.j@mail.ru
Tashkent, Uzbekistan
References
- Архангельский A. B. Аддиционная теорема для веса множеств, лежащих в бикомпактах// Докл. АН СССР. - 1959. - 126, № 2. - С. 239-241.
- Борсук К. Теория шейпов. - М.: Мир, 1976.
- Жураев Т. Ф. Некоторые геометрические свойства функтора P вероятностных мер и его подфункторов// Дисс. к.ф.-м.н. - М.: МГУ, 1989.
- Пономарев В. И. О непрерывных разбиениях бикомпактов// Усп. мат. наук. - 1957. - 12. - С. 335-340.
- Федорчук В. В. Вероятностные меры в топологии// Усп. мат. наук. - 1991. - 46, № 1. - C. 41-80.
- Шепин Е. В. Функторы и несчетные степени компактов// Усп. мат. наук. - 1981. - 36,№ 3. - С. 3-62.
- Kodama Y., Spiez S., Watanabe T. On shapes of hyperspaces// Fund. Math. - 1978. - 11.- С. 59-67.
- Mardesˇic´ S., Segal J. Shapes of compacta and ANR-systems// Fund. Math. - 1971. - 72. - С. 41-59.
- Mardesˇic´ S., Sеgal J. Equivalence of the Borsuk and the ANR-system approach to shapes// Fund. Math. - 1971. - 72. - С. 61-66.
- Mazurkiewicz S., Sierpin´ ski W. Contribution a` la topologie des ensembles de´nombrables// Fund. Math. - 1920. - 1, № 1. - С. 17-27.
- Mrozik P. Hereditary shape equivalences and complement theorems// Top. Appl. - 1986. - 22, № 1. - С. 131-137.
- Pelczyn´ ski A. A remark on spaces 2∗ for zerodimensional X// Bull. Acad. Polon. Scr. Sci. Math. Astronom. Phys. - 1965. - 19. - С. 85-89.
