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Let G be a semialgebraic group which is not necessarily compact. Let X be a semialgebraically proper G-set such that the orbit space has a semialgebraic structure. In this paper we prove the existence of semialgebraic slices of X. Moreover X can be covered by finitely many semialgebraic G-tubes.doi:10.5831/hmj.2015.37.4.431 fatcat:n7u7fbuyc5dmjniyjcbqqb3hpa