Hryniv O. Free and universal objects in the category of topological inverse semigroups

In the thesis universal objects in various classes of compact Clifford topological inverse semigroups are constructed; compact Clifford topological inverse semigroups that embed into hyperspaces over topological groups and into convolution and functor-semigroups over topological groups are characterized; it is proved that the construction of a free topological universal algebra of continuous signature preserves closed embeddings of metrizable (more generally stratifiable) spaces; conditions on a topological space guaranteeing that its free topological inverse semigroups in various classes of topological inverse semigroups are infinite dimensional manifolds are found.