A note on separation in AP

Authors

  • R. Lowen University of Antwerp
  • M. Sioen Free University of Brussels

DOI:

https://doi.org/10.4995/agt.2003.2046

Keywords:

Approach space, Separation property, Reflection

Abstract

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.

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Author Biographies

R. Lowen, University of Antwerp

Department of Mathematics and Computer Science

M. Sioen, Free University of Brussels

Department of Mathematics

References

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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Published

2003-10-01

How to Cite

[1]
R. Lowen and M. Sioen, “A note on separation in AP”, Appl. Gen. Topol., vol. 4, no. 2, pp. 475–486, Oct. 2003.

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