Implicit operations on DS

In this work we illustrate how the study of the topological semigroups of implicit operations of a pseudovariety V can be useful to the knowledge of V. In particular, for subpseudovarieties of DS, we find factorizations of the implicit operations in terms of regular and explicit ("words'') ones. For a better knowledge of V, we try to solve some kind of "word problem'' on V i.e., decide when two implicit operations are the same in V. Such study has already been done for some pseudovarieties, namely J, R and L. As an application of this study we calculate some joins of pseudovarieties