FILALI, MAHMOUD; PROTASOV, IGOR V. Ultrafilters and Topologies on Groups. VNTL Publishers, 2010. ISBN 9668849140, 150 x 225 mm, 258 pp., hand-made cloth binding.
The book is devoted to the studying of ultrafilters in topological algebra. The main object of investigations is the Stone-Cech compactification betaG of a topological group G. The set betaG is a right topological semigroup and the continuity of the operation involving the left translation is extensively studied in the book. The richness of algebraic structure, makes the semigroup betaG very useful and with plenty of applications in combinatorics as well as in functional analysis, in particular, to the left convolution algebras. In the book, the algebra in the Stone-Cech compactification is used to construct and study topologies on groups. Mathematical Studies: Monograph Series. Volume 13.