Functorial approach structures


  • Guillaume C.L. Brümmer University of Cape Town
  • M. Sioen Free University of Brussels



Approach space, (approach) bicompleteness, Epireflective subcategory, Functorial approach structure, Spanning, Topological space


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.


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Author Biographies

Guillaume C.L. Brümmer, University of Cape Town

Department of Mathematics and Applied Mathematics

M. Sioen, Free University of Brussels

Department of Mathematics


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How to Cite

G. C. Brümmer and M. Sioen, “Functorial approach structures”, Appl. Gen. Topol., vol. 4, no. 1, pp. 91–97, Apr. 2003.



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