On Jakovlev spaces (Q2382330)

A Jakovlev space is based on a construction of Jakovlev exhibiting a weakly first countable space which is not first countable, and is always a compact, Hausdorff, 0-dimensional, weakly first countable, scattered space of scattered height \(\omega+1\) and of sequential order 2, but not first countable. Jakovlev spaces are described of cardinality \(\mathfrak c\) and \(\mathfrak c^+\) when \(\mathfrak b= \mathfrak c\), and of cardinality \(\aleph_1\) when \(\aleph_1<2^ {\aleph_0}\). There is also a model constructed in which there are Jakovlev spaces of any cardinality of the form \(\kappa^{\aleph_0}\).