Metric spaces and textures

• Autores: Senol Dost
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 18, Nº. 1, 2017, págs. 203-217
• Idioma: inglés
• DOI: 10.4995/agt.2017.6889
• Enlaces
  • Texto completo
• Resumen

  • Textures are point-set setting for fuzzy sets, and they provide a framework for the complement-free mathematical concepts. Further dimetric on textures is a gener- alization of classical metric spaces. The aim of this paper is to give some properties of dimetric texture space by using categorical approach. We prove that the category of clas- sical metric spaces is isomorphic to a full subcategory of dimetric texture spaces, and give a natural transformation from metric topologies to dimetric ditopologies. Further, it is pre- sented a relation between dimetric texture spaces and quasi-pseudo metric spaces in the sense of J. F. Kelly. 

• Referencias bibliográficas
  • J. Adámek, H. Herrlich and G. E. Strecker, Abstract and concrete categories, John Wiley & Sons, Inc., 1990.
  • L. M. Brown and M. Diker, Ditopological texture spaces and intuitionistic sets, Fuzzy Sets and Systems 98 (1998), 217-224.
  • https://doi.org/10.1016/S0165-0114(97)00358-8
  • L. M. Brown and R. Ertürk, Fuzzy sets as texture spaces, I. Representation Theorems, Fuzzy Sets and Systems 110, no. 2 (2000), 227-236.
  • https://doi.org/10.1016/S0165-0114(98)00157-2
  • L. M. Brown and R. Ertürk, Fuzzy sets as texture spaces, II. Subtextures and quotient textures, Fuzzy Sets and Systems 110, no. 2 (2000),...
  • https://doi.org/10.1016/S0165-0114(98)00158-4
  • L. M. Brown, R. Ertürk and S. Dost, Ditopological texture spaces and fuzzy topology, I. Basic Concepts, Fuzzy Sets and Systems 147, no. 2...
  • https://doi.org/10.1016/j.fss.2004.02.009
  • L. M. Brown, R. Ertürk and S. Dost, Ditopological texture spaces and fuzzy topology, II. Topological Considerations, Fuzzy Sets and Systems...
  • https://doi.org/10.1016/j.fss.2004.02.010
  • L. M. Brown, R. Ertürk and S. Dost, Ditopological texture spaces and fuzzy topology, III. Separation Axioms, Fuzzy Sets and Systems 157, no....
  • https://doi.org/10.1016/j.fss.2006.02.001
  • M. Diker and A. Altay Ugur, Textures and covering based rough sets, Information Sciences 184 (2012), 33-44.
  • https://doi.org/10.1016/j.ins.2011.08.012
  • J. L. Kelley, General topology, D. Van Nostrand, Princeton, 1995.
  • M. Kule and S. Dost, A textural view of semi-separation axioms in soft fuzzy topological spaces, Journal of Intelligent Fuzzy Systems 32 (2017),...
  • https://doi.org/10.3233/JIFS-16140
  • S. Özcag and L. M. Brown, Di-uniform texture spaces, Applied General Topology 4, no. 1 (2003), 157-192.
  • S. Özcag and S. Dost, A categorical view of di-uniform texture spaces, Bol. Soc. Mat. Mexicana 15, no. 3 (2009), 63-80.
  • F. Yildiz, Completeness types for uniformity theory on textures, Filomat 29, no. 1 (2015), 159-178.
  • https://doi.org/10.2298/FIL1501159Y