On Hausdorff Extensions and Hausdorff Absolutes of an Orbit Space

Abstract

The paper is concerned with the study of Hausdorff extensions and Hausdorff absolutes of the orbit space of a Hausdorff G-space. Actions are induced on some Hausdorff extensions namely Katetov extension k(X) and Fomin extension σ(X) of a Hausdorff space X acted upon by a discrete group G. A natural question that whether the orbit space of an extension is the corresponding extension of the orbit space is answered in Section 3.