Metric spaces and textures
Submitted: 2016-11-20
|Accepted: 2017-02-15
|Published: 2017-04-03
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Keywords:
metric space, texture space, uniformity, natural transformation, difunction, isomorphism
Supporting agencies:
Abstract:
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.
References:
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), 237-245.
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 (2004), 171-199.
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 147, no. 2 (2004), 201-231.
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. 14 (2006), 1886-1912.
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), 925-936.
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.
