Equivariant compactifications of topological and bitopological transformation groups

Includes bibliographical references

Functorial approach structures

[EN] We show that there exists at least a proper class of functorial approach structures, i.e., right inverses to the forgetful functor T : AP→ Top (where AP denotes the topological construct of approach spaces and contractions as introduced by R. Lowen). There is however a great difference in nature of these functorial approach structures when compared to the quasi-uniform paradigm which has been extensively studied by the first author: whereas it is well-known from [2] that a large class of epireflective subcategories of Top0 can be “parametrized” using the interaction of functorial quasi-uniformities with the quasi-uniform bicompletion, we show that using functorial approach structures together with the approach bicompletion developed in [10], only Top0 itself can be retrieved in this way.Brümmer, GC.; Sioen, M. (2003). Functorial approach structures. Applied General Topology. 4(1):91-97. doi:10.4995/agt.2003.2012.SWORD91974