Kim, Eun-Seok;Ahn, Seung-Ho;Park, Dae-Heui

  • Received : 2011.01.18
  • Accepted : 2011.02.22
  • Published : 2011.03.25


This paper studies the relationship between L-fuzzy proximities and L-fuzzy topologies by topological fuzzy remote neigh-borhood systems. We will prove that the category of L-fuzzy topo- logical spaces can be embedded in the category of L-fuzzy quasi-proximity spaces as a core ective full subcategory.


L-fuzzy topology;L-fuzzy uniformity;L-fuzzy proximity;L-fuzzy topological order;fuzzy remote neighborhood systems


  1. Adamek J, Herrlich H, Strecker G E, Abstract and Concrete Categories, J. Wiley and Sons, New York, 1990.
  2. Artico G, Moresco R, Fuzzy proximities and totally bounded fuzzy uniformities, J. Math. Anal. Appl., 1984,9:320-1337.
  3. Artico G, Moresco R, Fuzzy proximities compatible with Lowen uniformities, Fuzzy Sets and Systems, 1987,21: 85-99.
  4. Fang J M, Yue Y L, ,Base and subbase in I-fuzzy topological spaces, J.Math.Res. Expositon, 2006, 26: 89-95.
  5. Ghanim M H, Tantawy O A, Selim F M, On S-fuzzy quasi-proximity spaces, Fuzzy Sets and Systems, 2000,109:285-290.
  6. Gierz G, et al., A compendium of continuous lattices, Berlin: Springer Verlag, 1980.
  7. Hutton B, Uniformities on fuzzy topological spaces, J. Math. Anal. Appl., 1977,58: 557-571.
  8. Katsaras A K, On fuzzy uniform spaces, J. Math. Anal. Appl., 1984, 101: 97-114.
  9. Kubiak T, On fuzzy topologies (PhD Thesis, Adam Mickiewicz, Poznan (Poland)), 1985.
  10. Liu W J, Fuzzy proximity spaces redefined, Fuzzy Sets and Systems, 1985, 15:241-248.
  11. Preuss G, Theory of topological structures: An approch to categorical topology, D.Reidel Publishing Company, 1987.
  12. Shi F G, The category of pointwise S-proximity spaces, Fuzzy Sets and Systems, 2005,152:349-372.
  13. Sostak A P, On a fuzzy topological structure, Rend. Cire. Matem. Palermo, Ser. II 1985,11:89-103.
  14. Yue Y L, Fang J M, Categories isomorphic to the Kubiak-Sostak extension of TML Fuzzy Sets and Systems, 2006,157: 832-842.
  15. Yue Y L, Shi F G, Generalized quasi-proximities, Fuzzy Sets and Systems, 2007,158:386-398