Strongly sequentially separable function spaces, via selection principles

2019/05/20 by Osipov, Alexander V., Szewczak, Piotr, Tsaban, Boaz
#03E75 #26A03 #37F20 #54C35 #FOS: Mathematics #Functional Analysis (math.FA) #General Topology (math.GN)

paper · doi:10.48550/arxiv.1905.08070

Abstract

A separable space is strongly sequentially separable if, for each countable dense set, every point in the space is a limit of a sequence from the dense set. We consider this and related properties, for the spaces of continous and Borel real-valued functions on Tychonoff spaces, with the topology of pointwise convergence. Our results solve a problem stated by Gartside, Lo, and Marsh.

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