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

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

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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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Section

Regular Articles