Ernest Schimmerling

Mathematical logic seminar - September 9, 2003

Time: 12 - 1:20 p.m.

Room: Physical Plant Bldg. 300

Speaker: Uri Abraham
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.