Strongly sequentially separable function spaces, via selection principles

Alexander V. Osipov, Piotr Szewczak, Boaz Tsaban

Published 2019-05-20Version 1

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.