TY - JOUR
AU - Brümmer, Guillaume C.L.
AU - Sioen, M.
PY - 2003/04/01
Y2 - 2024/08/04
TI - Functorial approach structures
JF - Applied General Topology
JA - Appl. Gen. Topol.
VL - 4
IS - 1
SE -
DO - 10.4995/agt.2003.2012
UR - https://polipapers.upv.es/index.php/AGT/article/view/2012
SP - 91-97
AB - <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>
ER -