DOI QR코드

DOI QR Code

(L,⊙)-quasi-uniform Spaces and (L,⊙)-neighborhood Systems

  • Kim, Yong-Chan (Department of Mathematics, Kangnung-Wonju National University) ;
  • Ko, Jung-Mi (Department of Mathematics, Kangnung-Wonju National University)
  • 투고 : 2009.03.17
  • 심사 : 2009.05.07
  • 발행 : 2009.06.30

초록

In this paper, we introduced the notion of (L,$\bigodot$)-quasi-uniform spaces and (L,$\bigodot$)-neighborhood systems on a strictly two-sided, commutative quantale lattice L. We investigate their properties and give the examples. In particular, we study the relations between (L,$\bigodot$)-quasi-uniform spaces and (L,$\bigodot$)-neighborhood systems.

키워드

참고문헌

  1. A. Craig, G. Jager, "A common framework for latticevalued uniform spaces and probabilistic uniform limit spaces", Fuzzy Sets and Systems, vol. 158, pp. 424-435, 2007 https://doi.org/10.1016/j.fss.2006.10.016
  2. J. Gutierrez Garcia, M. A. de Prade Vicente, A.P. Sostak, A unified approach to the concept of fuzzy L-uniform spaces, Chapter 3 in [11], pp. 81-114
  3. U. H$\ddot{o}$hle, E. P. Klement, Non-classical logic and their applications to fuzzy subsets, Kluwer Academic Publisher, Boston, 1995
  4. U. H$\ddot{o}$hle, S. E. Rodabaugh, Mathematics of Fuzzy Sets, Logic, Topology and Measure Theory, The Handbooks of Fuzzy Sets Series, Volume 3, Kluwer Academic Publishers, Dordrecht, 1999
  5. B. Hutton, "Uniformities on fuzzy topological spaces," J. Math. Anal. Appl., vol. 58, pp. 559-571, 1977 https://doi.org/10.1016/0022-247X(77)90192-5
  6. U.Hohle, A.P.Sostak, Axiomatic foundation of fixedbasis fuzzy topology, Chapter 3 in [4], 123-272
  7. Y.C. Kim, Y.S. Kim, "(L, $\bigodot$)-approximation spaces and (L, $\bigodot$)-fuzzy quasi-uniform spaces," Information Sciences, vol. 179, pp.2028-2048, 2009 https://doi.org/10.1016/j.ins.2009.02.003
  8. W. Kotze, Uniform spaces, Chapter 8 in [4], pp. 553-580
  9. Liu Ying-Ming, Luo Mao-Kang, Fuzzy topology, World Scientific Publishing Co., Singapore, 1997
  10. C.J. Mulvey, Quantales, Suppl. Rend. Cric. Mat. Palermo Ser.II 12, pp. 99-104, 1986
  11. S. E. Rodabaugh, E. P. Klement, Topological And Algebraic Structures In Fuzzy Sets, The Handbook of Recent Developments in the Mathematics of Fuzzy Sets, Trends in Logic 20, Kluwer Academic Publishers, (Boston/Dordrecht/London), 2003
  12. D. Zhang, "A comparison of various uniformities in fuzzy topology," Fuzzy Sets and Systems, vol. 159, pp. 2503-2519, 2008 https://doi.org/10.1016/j.fss.2008.03.003