@article{Brümmer_Sioen_2003, title={Functorial approach structures}, volume={4}, url={https://polipapers.upv.es/index.php/AGT/article/view/2012}, DOI={10.4995/agt.2003.2012}, abstractNote={<p>We show that there exists at least a proper class of functorial approach structures, i.e., right inverses to the forgetful functor T : APâ†’ 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 Top<sub>0</sub> 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 Top<sub>0</sub> itself can be retrieved in this way.</p>}, number={1}, journal={Applied General Topology}, author={Brümmer, Guillaume C.L. and Sioen, M.}, year={2003}, month={Apr.}, pages={91–97} }