A Wallman-Shanin-Type Compactification for Approach Spaces

Abstract

In [11] a Cech-Stone-type compactification theory was developed for UAP2. In this paper we construct a Wallman-Shanin-type compactification theory for weakly symmetric T1 approach spaces which form a full subcategory of AP properly containing UAP2. For a weakly symmetric T1 approach space, we also investigate the relation between the topological bicoreflection of its Wallman-type compactification and the classical Wallman compactification of its topological bicoreflection, and we show that our theory extends the classical topological Wallman compactification theory. It is shown in [14] that our present theory also extends the CechStone-type theory from [11].