| Time: | 12 - 1:20 p.m. |
| Room: |
Physical Plant Bldg. 300
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| 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
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| 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.
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| Organizer's note: | Please bring your lunch.
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