Strongly sequentially separable function spaces, via selection principles
General Topology
2019-11-11 v2 Functional Analysis
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.
Cite
@article{arxiv.1905.08070,
title = {Strongly sequentially separable function spaces, via selection principles},
author = {Alexander V. Osipov and Piotr Szewczak and Boaz Tsaban},
journal= {arXiv preprint arXiv:1905.08070},
year = {2019}
}
Comments
9 pages