Smooth uniform spaces

  • Ramadan, A.A. (Department of Mathematics, Faculty of Science, Cairo University, Beni-Suef, Egypt) ;
  • El-Dardery, M. (Department of Mathematics, Faculty of Science, Cairo University, Faiyum, Egypt) ;
  • Kim, Y.C. (Department of Mathematics, Kangnung National University)
  • Published : 2002.03.01


We study some properties of smooth uniform spaces. We investigate the relationship between smooth topological spaces and smooth uniform spaces. In particular, we define a subspace of a smooth uniform space and a product of smooth uniform spaces.



  1. G. Artico and R. Moresco, 'Fuzzy proximities and totallybounded fuzzy uniformhies,' J. Math. AnaI. Appl., vol. 99,pp. 320-337, 1984
  2. R. Badard, A. A. Ramadan and A. S. Mashhour, 'Smoothpreuniform and preproximity spaces,' Fuzzy Sets and Sys-tems, vol. 59, pp. 95-107, 1993
  3. C.L. Chang, 'Fuzzy topological spaces,' J. Math. Anal. Appl, vol. 24, pp. 182-190, 1968
  4. M.K. El Gayyer, E.E. Kere and A.A. Ramadan, 'Almost compactness and near compactness in smooth topological spaces,' Fuzzy Sets and Systems, vol. 62, pp. 193-202, 1994
  5. J.Gutierrez Garcia, Mardoness Perez and M. H.Burton,'The relation between various filter notions on a GL-monoid,' J. Math. Anal. Appl, vol. 230, pp.291-302, 1999
  6. U. Hohle and S. E. Rodabaugh, Mathenatics of Fuzzy Sets:Logic, Topology, and Measure theory, The Handbooks of Fuzzy sets series, Volume 3, Kluwer Academic Publishers, Dordrecht (1999)
  7. U. Hohle and A. Sostak, Axiomatic foundations of fixed-basis fuzzy topology, in (6)
  8. A. K. Katsaras, 'On fuzzy uniform spaces,' J. Math. Anal.Appl, vol. 101, pp.97-113, 1984
  9. Y.C. Kim, 'Initial smooth fuzzy topological spaces,' J. of Korea Fuzzy Logic and Intelligent Systems, vol. 8,no. 3, pp.88-94, 1998
  10. W. Kotze, 'Uniform spaces,' in (6)
  11. Liu Ying-Ming and Luo Mao-Kang, Fuzzy topology, World Scientific Publishing, Singapore, 1997
  12. R. Lowen, 'Fuzzy topological spaces and fuzzy com-pactness,' J. Math Anal. Appl, .vol. 56, pp. 621-633, 1976
  13. A.A. Ramadan, 'Smooth topological spaces,' Fuzzy Setsand Systems, vol. 48, pp. 371-375, 1992
  14. A.A. Ramadan, Y. C. Kim and M.K. El-Gayyar, 'On Fuzzy Uniform Spaces,' (submit to J of fuzzy Mathematics)
  15. A.P.Sostak, 'On a fuzzy topological structure,' Suppl. Rend. Circ. Mat Palermo Ser. II, 11, pp. 89-103, 1985
  16. A.P.Sostak, 'On some modifications of fuzzy topo-logies,' Mat Vesnik, vol. 41, pp. 51-64, 1989