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 ${\exp }_{\beta }f:{\exp }_{\beta }X\to {\exp }_{\beta }Y$ is superparacompact iff a given map $f:X\to Y$ is superparacompact.

8 pages