On construction of global actions for partial actions

摘要

Every partial action a on a set has a unique minimal globalization (up to equivalence [4]). In [2], the authors proved that {(G, X_G), i} is a unique minimal globalization of a which is equivalent to left coset action (G, G/G_x) for any x ∈ X, if a is a transitive partial action. In this paper, we construct a unique minimal global action of a given partial action which is equivalent to (G, U_(s∈S)G/G_s), where S is a G-transversal in X without resorting to transitivity so that a minimal global action can be constructed for a larger class of partial actions on sets. We also study the Hausdroff topology on a minimal globalization.