A note on separation in AP

• Lowen, R. ^[1] ; Sioen, M. ^[2]
  1. [1] University of Antwerp

     University of Antwerp

     Arrondissement Antwerpen, Bélgica

     
  2. [2] Free University of Brussels
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 4, Nº. 2, 2003, págs. 475-486
• Idioma: inglés
• DOI: 10.4995/agt.2003.2046
• Enlaces
  • Texto completo
• Resumen

  • 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.

• Referencias bibliográficas
  • 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...
  • 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...
  • 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)