Hyperspaces of Superparacompact Spaces and Continuous Maps
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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