Hyperspaces of Superparacompact Spaces and Continuous Maps

Year 2019, Volume: 2 Issue: 2, 65 - 69, 28.06.2019

Adilbek Zaitov , Davron İlxomovich Jumaev

https://doi.org/10.32323/ujma.481052

Cited By: 2

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

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