Abstract:We prove that $\diamondsuit^*$ implies there is a zero-dimensional Hausdorff Lindel\"of space of cardinality $2^{\aleph_1}$ which has points $G_\delta$. In addition, this space has the property that it need not be Lindel\"of after countably closed forcing.
Keywords: Lindel\"of; forcing
DOI: DOI 10.14712/1213-7243.2015.119
AMS Subject Classification: 54D20 54A25