A generalized theory of expansions and collapses with applications to Z-compactification

Abstract

We generalize the dual notions of "expansion" and "collapse" so they can be applied to arbitrary metric spaces. We also expand the theory to allow for infinitely many such moves. Those tools are then employed to prove a variety of compactification theorems. We are particularly interested in Z-set compactifications, which play an important role in geometric group theory and in algebraic and geometric topology.