Hyperspaces of Superparacompact Spaces and Continuous Maps

Authors : Adilbek ZAİTOV, Davron İlxomovich JUMAEV

Pages : 65-69

Doi:10.32323/ujma.481052

View : 19 | Download : 9

Publication Date : 2019-06-28

Article Type : Research Paper

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