Absolute $F_{σδ}$ spaces

Vojtěch Kovařík, Ondřej Kalenda

Published 2017-03-08Version 1

We prove that hereditarily Lindel\"of space which is $F_{\sigma\delta}$ in some compactification is absolutely $F_{\sigma\delta}$. In particular, this implies that any separable Banach space is absolutely $F_{\sigma\delta}$ when equipped with the weak topology.