Ernest Schimmerling

### Mathematical logic seminar - September 9, 2003

 Time: 12 - 1:20 p.m. Room: Physical Plant Bldg. 300 Speaker: Uri Abraham Professor Department of Mathematics Ben-Gurion University of the Negev Visiting Professor Department of Mathematical Sciences Carnegie Mellon University Title: On Jakovlev Spaces Abstract: A topological space $X$ is called weakly first countable, if for every point $x$ there is a countable family $\{C_n^x \mid n\in\omega\}$ such that $x\in C_{n+1}^x \subseteq C_n^x$ and such that $U \subset X$ is open iff for each $x \in U$ some $C_n^x$ is contained in $U$. This weakening of first countability is due to A. V. Arhangelskii from 1966, who asked whether compact weakly first countable spaces are first countable. In 1976, N.N. Jakovlev gave a negative answer under the assumption of continuum hypothesis. His result was strengthened by V.I. Malykhin in 1982, again under CH. In our lecture we survey these results, describe some extensions obtained with I. Gorelic, and state some open questions. Organizer's note: Please bring your lunch.