- Universal Journal of Mathematics and Applications
- Vol: 2 Issue: 2
- Hyperspaces of Superparacompact Spaces and Continuous Maps
Hyperspaces of Superparacompact Spaces and Continuous Maps
Authors : Adilbek Zaitov, Davron Ilxomovich Jumaev
Pages : 65-69
Doi:10.32323/ujma.481052
View : 9 | Download : 4
Publication Date : 2019-06-28
Article Type : Research
Abstract :In the present paper we establish that the space $\exp_\beta X$ of compact subsets of a Tychonoff space $X$ is superparacompact iff $X$ is so. Further, we prove the Tychonoff map $\exp_{\beta} f:\ \exp_{\beta} X\rightarrow \exp_{\beta} Y$ is superparacompact iff a given map $f:\ X\rightarrow Y$ is superparacompact.Keywords : Finite-component cover, Hyperspace, Superparacompact space, Tychonoff map