**Department of Mathematics**

**"** **On West
Compactifications of Locally Compact Abelian Groups****"**

By

**ELÇİM ELGÜN**

**(LAKEHEAD UNIVERSITY, CANADA)**

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**Abstract: ** **It is known that, using an idea of T. T. West,
the unit ball of ***L*^{∞ }**[0,
1] can be identified as a compactification of ***Z*. In this talk, we will generalize this result to any locally
compact Abelian group G. Depending on the algebraic properties of *G*, we will construct a semigroup
compactification as a certain compact sub semigroup of *L*^{∞}** [0,1],
which is a quotient of both the Eberlein compactification, ***G*^{e}**,
and the weakly almost periodic compactification, ***G*^{w} of *G*. The concrete structure of these
compact quotients allows us to gain insight into known results by G. Brown, W.
Moran, J. Pym and B. Bordbar, where for groups *G = Z* and *G = Z*^{∞}_{q}_{ }**, it is proved that ***G*^{w} contain uncountably many idempotents and
the set of idempotents is not closed.

** **

** **

**Date: ****Monday, March 7, 2016**

**Time: ****15.40**

**Place: ****Mathematics Seminar Room,
SA-141**

Tea and cookies will be served before the
seminar.