On embeddings of proper and equicontinuous actions in zero-dimensional compactifications

On Embeddings of Proper and Equicontinuous Actions in Zero-dimensional Compactifications

We provide a tool for studying properly discontinuous actions of non-compact groups on locally compact, connected and paracompact spaces, by embedding such an action in a suitable zero-dimensional compactification of the underlying space with pleasant properties. Precisely, given such an action (G,X) we construct a zero-dimensional compactification μX of X with the properties: (a) there exists ...

Zero-dimensional proximities and zero-dimensional compactifications

Article history: Received 4 August 2008 Received in revised form 12 December 2008 Accepted 13 December 2008 MSC: 54E05 54D35 54G05

compactifications and function spaces on weighted semigruops

chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...

Compactifications of Dimension Zero

compactifications and representations of transformation semigroups

this thesis deals essentially (but not from all aspects) with the extension of the notion of semigroup compactification and the construction of a general theory of semitopological nonaffine (affine) transformation semigroup compactifications. it determines those compactification which are universal with respect to some algebric or topological properties. as an application of the theory, it is i...