Hyperspaces of superparacompact spaces and continuous maps

2018/10/29 by Zaitov, Adilbek, Jumaev, Davron
#54B20 #54C10 #FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.1811.05347

Abstract

In the present paper we establish that the space exp_βX of compact subsets of a Tychonoff space X is superparacompact iff X is so. Further, we prove the Tychonoff map exp_β f: exp_β X→ exp_β Y is superparacompact iff a given map f: X→ Y is superparacompact.

Related

• A note on hyperspaces and the compact-open topology
• On Tychonoff-type hypertopologies
• Yet another proof of Tychonoff's Theorem
• Maximal almost disjoint families and pseudocompactness of hyperspaces
• The hyperspaces HS(p,X)