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A Coarse Approach To The Freudenthal Compactification And Ends Of Groups, Hussain S. Rashed

Doctoral Dissertations

The main purpose of this work is to present a coarse counterpart to the Freudenthal compactification and its corona (the space of ends) that generalizes the Freudenthal compactification of a Freudenthal topological space X (connected, locally connected, locally compact and σ-compact) and its corona; then applying it to groups as coarse space to obtain generalizations to many well-known results in the theory of ends of groups. To this end, we present two constructions:

1. The Coarse Freudenthal compactification of a proper metric space which is a coarse compactification that coincides with the Freudenthal compactification when the metric space is geodesic. …