StatusThe thesis was presented on the 19 November, 2009
Approved by NCAA on the 11 February, 2010
Abstract– 0.32 Mb / in romanian
The thesis is dedicated to the study of the general problems of the theory of extensions of the topological universal algebras from the topological point of view. In particular, the concept of almost periodicity on a universal algebra is investigated.
Objectives of the thesis are: the elaboration of the concept of the almost periodicity on a universal algebra; the investigation of the classes of almost periodic functions on a given universal algebra; the construction of the compact algebraical extensions of topological universal algebras.
In the thesis there are solved the next problems: the elaboration of the methods of research of the spaces of almost periodic functions; the construction of the special compactifications of the n-ary topological groupoids.
There are established: the space of (weakly) almost periodic functions is a Banach space; the space of (weakly) almost periodic mappings is complete; the space of weakly almost periodic functions generates the Bohr compactification proposed by Alfsen and Holm; the space of almost periodic functions is determined by the stable totally bounded pseudometrics.
The basic results are new. The notion of complete compactity is essential.
In the thesis, in particular, there are solved some concrete problems arised
by J.E.Hart, K.Kunen and A.Cashu. Thee concept of the almost periodicity is
based on the notions of the semigroup of translations and the oriented semigroup
of translations. This new point of view permits to establish the concepts of
almost periodicity and weakly almost periodicity on any universal algebra. For
each universal algebra the Weil’s reduction is obtained.