2021/10/18 by Taras Banakh, Banakh, Taras, Saak Gabriyelyan +1
Mathematics · #03E65 #28A33 #54A35 #54D30 #FOS: Mathematics #Functional Analysis (math.FA) #General Topology (math.GN) #Logic (math.LO) #math.FA #math.GN #math.LO #msc:03E65 #msc:28A33 #msc:54A35 #msc:54D30
paper · pdf · doi:10.48550/arxiv.2110.09062
21 pages
arxiv created 2021/10/18 · arxiv updated 2021/10/19
Under Jensen's diamond principle \diamondsuit, we construct a simple Efimov space K whose space of nonatomic probability measures Pna(K) is first-countable and sequentially compact. These two properties of Pna(K) imply that the space of probability measures P(K) on K is selectively sequentially pseudocompact and the Banach space C(K) of continuous functions on K has the Gelfand-Phillips property. We show also that any sequence of probability measures on K that converges to an atomic measure converges in norm, and any sequence of probability measures on K converging to zero in sup-norm has a subsequence converging to a nonatomic probability measure.