Are Eberlein-Grothendieck scattered spaces $\sigma$-discrete?

Antonio Avilés; David Guerrero Sánchez

Are Eberlein-Grothendieck scattered spaces $\sigma$-discrete?

General Topology 2012-02-29 v1

Authors: Antonio Avilés , David Guerrero Sánchez

Abstract

A space $X$ is Eberlein-Grothendieck if $X\subset C_p(K)$ for some compact space $K.$ In this paper we address the problem of whether such a space $X$ is $\sigma$ -discrete whenever it is scattered. We show that if $w(K)\leq\omega_1$ then $X$ is $\sigma$ -dicrete whenever $X$ has height $\omega_1$ and it is locally compact or locally countable. It is also proved that every Lindel\"of \v{C}ech-complete scattered space is $\sigma$ -compact.

Keywords

general topology

Cite

@article{arxiv.1202.6310,
  title  = {Are Eberlein-Grothendieck scattered spaces $\sigma$-discrete?},
  author = {Antonio Avilés and David Guerrero Sánchez},
  journal= {arXiv preprint arXiv:1202.6310},
  year   = {2012}
}

Related papers

View all related →