Some topological properties of fuzzy cone metric spaces

Volume 9, Issue 3, pp 799--805 http://dx.doi.org/10.22436/jnsa.009.03.08

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 1837 Downloads
• 3711 Views

Authors

Tarkan Öner - Department of Mathematics, Faculty of Sciences, Muğla Sıtkı Koçman University, 48000 Mugla, Turkey.

Abstract

We prove Baire's theorem for fuzzy cone metric spaces in the sense of Öner et al. [T. Öner, M. B. Kandemir, B. Tanay, J. Nonlinear Sci. Appl., 8 (2015), 610-616]. A necessary and sufficient condition for a fuzzy cone metric space to be precompact is given. We also show that every separable fuzzy cone metric space is second countable and that a subspace of a separable fuzzy cone metric space is separable.

Share and Cite

Keywords

• Fuzzy cone metric space
• Baire's theorem
• separable
• second countable.

MSC

•  54A40
•  54E35
•  54E15
•  54H25

References

• [1] T. Bag, Fuzzy cone metric spaces and fixed point theorems of contractive mappings, Ann. Fuzzy Math. Inform., 6 (2013), 657-668.


• [2] Z. Deng, Fuzzy pseudo-metric spaces, J. Math. Anal. Appl., 86 (1982), 74-95.


• [3] M. A. Erceg, Metric spaces in fuzzy set theory , J. Math. Anal. Appl., 69 (1979), 205-230.


• [4] A. George, P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems, 64 (1994), 395-399.


• [5] A. George, P. Veeramani , On some results of analysis for fuzzy metric spaces, Fuzzy Sets and Systems, 90 (1997), 365-368.


• [6] V. Gregori, S. Romaguera, Some properties of fuzzy metric spaces, Fuzzy Sets and Systems, 115 (2000), 485-489.


• [7] L. G. Huang, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332 (2007), 1468-1476.


• [8] O. Kaleva, S. Seikkala, On fuzzy metric spaces, Fuzzy Sets and Systems, 12 (1984), 215-229.


• [9] O. Kramosil, J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetika, 11 (1975), 336-344.


• [10] T. Öner, M. B. Kandemir, B. Tanay , Fuzzy cone metric spaces, J. Nonlinear Sci. Appl., 8 (2015), 610-616.


• [11] S. Rezapour, R. Hamlbarani , Some notes on the paper: ''Cone metric spaces and fixed point theorems of contractive mappings'', J. Math. Anal. Appl., 332 (2007), 1468-1476.


• [12] B. Schweizer, A. Sklar, Statistical metric spaces , Pacific J. Math., 10 (1960), 313-334.


• [13] L. A. Zadeh , Fuzzy sets, Information and Control, 8 (1965), 338-353.