Compactification: Limit Tower Spaces

摘要

Convergence approach spaces, defined by E. Lowen and R. Lowen, possess both quantitative and topological properties. These spaces are equipped with a structure which provides information as to whether or not a sequence or filter approximately converges. P. Brock and D. Kent showed that the category of convergence approach spaces with contractions as morphisms is isomorphic to the category of limit tower spaces. It is shown below that every limit tower space has a compactification. Moreover, a characterization of the limit tower spaces which possess a strongly regular compactification is given here. Further, a strongly regular S-compactification of a limit tower space is studied, where S is a limit tower monoid acting on the limit tower space.