Partial actions on quotient spaces and globalization

Abstract

[EN] Given a partial action of a topological group G on a topological space X we determine properties P which can be extended from X to its globalization. We treat the cases when P is any of the following: Hausdorff, regular, metrizable, second countable and having invariant metric. Further, for a normal subgroup H, we introduce and study a partial actionof G/H on the orbit space X/∼H, applications to invariant metric sand inverse limits are presented.