A note on separation in AP

R. Lowen, M. Sioen


It is our aim in this note to take a closer look at some separation axioms in the construct AP of approach spaces and contractions. Whereas lower separation axioms seem to be qualitative, the higher ones seem to have a quantitative nature. Also some characterizations for the corresponding epireectors will be given.


Approach space; Separation property; Reflection

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Adámek, J. Herrlich, H. and Strecker, G. Abstract and Concrete Categories, John Wiley, New York (1990)

Bentley, H. L., Herrlich H. and Lowen-Colebunders E. Convergence , J. Pure Appl. Alg. 68 (1990), pp. 27-45 http://dx.doi.org/10.1016/0022-4049(90)90130-A

Herrlich, H. Topological Structures, Math. Centre Tracts 52 (1974), pp. 59-122

Herrlich, H. Categorical Topology 1971-1981, Proc. 5th Prague Top. Symp. 1981, Heldermann Verlag Berlin (1983), pp. 279-383

Brock, P and Kent, D. On Convergence Approach Spaces, Appl. Cat. Struct. 6 (1998), pp. 117-125 http://dx.doi.org/10.1023/A:1008612905619

Kannan, V. On a Problem of Herrlich, J. Madurai. Univ. 6 (1976), pp. 101-104

Lowen, R. Approach Spaces: a Common Supercategory of TOP and MET, Math. Nachr. 141 (1989), pp. 183-226 http://dx.doi.org/10.1002/mana.19891410120

Lowen, R. Approach Spaces: the Missing Link in the Topology-Uniformity-Metric Triad, Oxford Mathematical Monographs, Oxford University Press (1997)

Lowen, E and Lowen, R. A Quasitopos Containing CONV and MET as full subcategories, Int. J. Math. and Math. Sci., 11(3) (1988), pp. 417-438 http://dx.doi.org/10.1155/S016117128800050X

Marny, T. On Epireective Subcategories of Topological Categories, Gen. Top. Appl. 10 (1979), pp. 175-181 http://dx.doi.org/10.1016/0016-660X(79)90006-0

Robeys, K., Extensions of Products of Metric Spaces, PhD Thesis Universiteit Antwerpen, RUCA (1992)

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1. Concrete functors determined by their restrictions to the T0 objects
G.C.L. Brümmer, H.-P.A. Künzi, M. Sioen
Topology and its Applications  vol: 158  issue: 17  first page: 2382  year: 2011  
doi: 10.1016/j.topol.2011.03.014

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Universitat Politècnica de València

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