Some Topological Properties in M-Fuzzy Metric Space

# Thaneswor Bhandari^{1} and Narayan Parasad Pahari^{2}

^{1}Department of Mathematics, Tribhuvan University, Butwal Multiple Campus, Butwal, Nepal.

^{2}Central Department of Mathematics, Institute of Science and Technology, Tribhuvan University, Kathmandu, Nepal.**Abstract:** This paper concerns our sustained efforts for introduction of $M$-fuzzy metric spaces and study their basic topological properties. As an application of this concept, we prove some convergences and continuous properties related on $M$-fuzzy metric spaces and introduce some related examples in support of our results.

**Keywords:** $M$-Fuzzy metric space, $D$-metric space, continuous t-norm, convergence.

**Cite this article as:** Thaneswor Bhandari and Narayan Parasad Pahari, *Some Topological Properties in M-Fuzzy Metric Space*, Int. J. Math. And Appl., vol. 9, no. 2, 2021, pp. 63-68.

**References**

- B. C. Dhang, Generalised metric spaces and mappings with fixed point, Bull. Calcutta Math. Sos., 84(4)(1992), 329-336.
- A. George and P. Veeramani, On some results on fuzzy metric space, Fuzzy Sets Syst, 64(1994), 395-404.
- V. Gregori and A. Sapena, On fixed point theoremin fuzzy metric spaces, Fuzzy Sets and Sys, 125(2002), 245-252.
- I. Kramosil and J. Michalek, Fuzzy metric and statical metric spaces, Kybernetica, 11(1975), 326-334.
- D. Mihet, A Banach contraction theorem in fuzzy metric spaces, Fuzzy Sets Sys, 144(2004), 431-439.
- B. E. Rhoades, A fixed point theorem for generalised metric spaces, Int. J. Math. Math. Sci., 19(1996), 145-153.
- R. Saadait and J. H. Park, On the intuitionistic fuzzy topological spaces, Choas, Solitons and Fractals, 27(2006), 331-344.
- B. Schweizer, H. Sherwood and R. M. Tardiff, Contractions on PM-space examples and counterexamples, Stochastica, 1(1988), 5-17.
- B. Sing and R. K. Sharma, Common fifed points via compatible maps in $D$-metric spaces, Rad. Mat., 11(2002), 145-153.
- L. A. Zadesh, Fuzzy sets, Inform and Control, 8(1965), 407-422.