Ascoli's theorem for pseudocompact spaces

2020/04/08 by Gabriyelyan, Saak · 1 citation
#54A05 #54B05 #FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.2004.03911

Abstract

A Tychonoff space X is called (\em sequentially) \em Ascoli if every compact subset (resp. convergent sequence) of C_k(X) is equicontinuous, where C_k(X) denotes the space of all real-valued continuous functions on X endowed with the compact-open topology. The classical Ascoli theorem states that each compact space is Ascoli. We show that a pseudocompact space X is Asoli iff it is sequentially Ascoli iff it is selectively ω-bounded.

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