Moscow--Petersburg seminar on low-dimensional mathematics
SPb, PDMI, room 311, 21.12.2001, 16:00--17:45
A.M.Vershik.
Universality and Universal Objects
(Urysohn's Space, Hall's Group, Erd\"os' Graph).
Universal objects in mathematics
(universal coverings, universal enveloping algebras,
terminal objects in a category etc.),
apart from their role in solving concrete problems,
are even more useful in giving a general view of the
theory and formulating good questions.
The talk is dedicated to the following three universal objects
which are quite important but up to now were very little studied.
-- the universal Polish (i.e. complete separable metric) space
defined 80 years ago by P.S.~Urysohn.
-- the universal locally finite group
defined 50 years ago by Ph.~Hall.
-- the universal infinite graph
defined 30 years ago by P.~Erd\"os.
We ought to study and use these objects.
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Seminar home page: http://www.pdmi.ras.ru/~duzhin/LDM