Some topics in topological algebra (Q1314677)

Free topological algebras over a given topological space \(X\) are considered. In the case when the signature \(E\) is a \(k_ \omega\)-space and \(K\) is a (complete) \(\beta\)-quasivariety of topological \(E\)-algebras, the author gives some conditions on \(X\) which imply countable tightness (the \(k\)-property, etc.) of the free topological \(E\)-algebra \(F(X,K)\). The relation of \(M_ K\)-equivalence between topological spaces is also studied in the paper. The majority of the results is completely analogous to those for free topological groups.