### REGULAR FUZZY BICLOSURE SPACES

#### Abstract

The concept of regular fuzzy closure spaces was introduced by R. Navalakhe. Here we have introduced and studied the concept of regular fuzzy biclosure spaces. The concept of generalized regular fuzzy biclosure spaces was earlier introduced by U.D Tapi and R. Navalakhe. Here we defined the concept of regular fuzzy biclosure space. We have compared our definition of regular fuzzy biclosure spaces with the other existing definitions. Our definition of regular fuzzy biclosure space satisfies basic desirable properties. We define sum product and subspace of regular fuzzy biclosure spaces. Some of these properties are continuous image of regular biclosure spaces are regular, closed subspace of regular space is regular. Product of regular fuzzy biclosure spaces is regular fuzzy biclosure space. It is also satisfy good extension properties. Some more relevant results related to regular biclosure space are also obtained.

*Key words**-*fuzzy biclosure spaces, fuzzy closure spaces, generalized regular fuzzy biclosure spaces, good extension property, product of regular fuzzy biclosure spaces, regular fuzzy biclosure spaces, subspace and sum of regular fuzzy biclosure spaces.*AMS Subject classification:* - 54A40

#### Full Text:

PDF#### References

Benchalli, S. S., Rayanagoudar, T. D. and Patil, P. G. (2009) g*- Pre regular and g* Pre normal spaces, International Mathematical Forum, vol 4, no 48, pp-2399-2408.

Birkhoff G. (1967) Lattice theory, Amer. Math. Soc. Colloq. Publ., vol. 25, Amer. Math. Soc., Providence, RI.

Boonpok, C. (2010) Generalized Regular Biclosure Spaces, International Mathematical Forum, vol 5, pp 723-729.

Boonpok C. (2009) On continuous maps in closure space, General mathematics vol 17 no 2, pp 127-134.

Cech.E.( 1966) Topological Spaces, Academice, Prague.

Chandrasekhararao, K. (2013) On Almost regular spaces, International Journal of Math. Analysis, vol 7 no 38, pp 1857-1862.

Dorsett, C. (1982) Semi regular spaces, Soochow J. Math.,vol 8, pp 45-53.

Dorsett, C. (1989) Semi regular and Semi normal spaces, Soochow Journal of Mathematics, vol 15, no 2, pp 223-231.

Kelly, J. C., (1963) Bitopological spaces, Proc. London Math. Soc. vol 13, pp 71-89.

Khan, M. and Hussain, M. (2009) On closed sets and normal spaces. Pk. ISSN 0022- 2941, Coden JNSMAC, vol48, no 1&2, pp 31- 41.

Maheswari, S. N. and Prasad, R. (1975) On s-regular spaces, Glansnik Mat.Ser.IIIvol 10, no 30, pp 347-350.

Mariappa, K. and Sekar, S. (2013) On Regular generalized b-closed set, International Journal of Math. Analysis,vol 7, no 13, pp 613-624.

Mashhour A.S., Ghanim M.H. (1985) Fuzzy closure spaces, J.Math. Anal. Appl. vol 106, pp 154-170.

Mishra, S., Bhardwaj, N., Joshi, V. (2012) On regular generalized weakly (rgw) - closed sets in topological spaces, International Journal of Math. Analysis, vol 6, no 39, pp 1939-1952.

Missier, S. P. and Robert, A. (2014) Higher separation axioms via semi *- open sets, International Journal of Engineering and Science, vol 4, no 6, pp 37-45.

Navalakhe, R. (2016) Regular fuzzy closure spaces, International Journal of Science Technology and Management,vol 5, pp 162-166.

Padma, P. and Udayakumar, R. (2015) On regular spaces and normal spaces, Journal of Progressive Research in Mathematicsvol 1, no 1.

Padma, P. and Udayakumar, R. (2015) OnQ^* S- regular spaces and Q^* S- normal spaces, Journal of Progressive Research in Mathematics vol 1, no 1.

Park, J. K. and Park, J. H. (2004) Mildly generalized closed sets, almost normal and mildly normal spaces, Chaos, Solitions and Fractals, vol 20,pp 1103-1111.

Srivastava R., Srivastava A.K. Choubey A., (1994) Fuzzy closure spaces, J. Fuzzy Math. vol2, pp 525-534.

Srivastava R., Srivastava M. (2000) On T0–and T1- fuzzy closure spaces, Fuzzy Sets and Systems. vol109, pp 263-269.

Srivastava, R. and Srivastava, M. (1997) on pairwise Hausdorff fuzzy bitopological spaces, J. Fuzzy Math.vol 5, no 3, pp 553-564.

Srivastava, M., Tripathi, R. (2016) On fuzzy pairwise- T0 and fuzzy pairwise – T1 Biclosure spaces, International journal of Mathematical Archive, vol 7, no 13, pp 09-15.

Srivastava, M., Tripathi, R., and Agrawal, A. K. (2017) On the concept of Hausdorffness in fuzzy biclosure space, International journal of current research, vol 9, no 02, pp46087-46090.

Tapi U.D. and Navalakhe, R. (2011) on fuzzy biclosure spaces, Int.J. Of Math. Anal. vol5,pp 789-795.

Tapi, U. D. and Navalakhe, R. (2012) Generalized Regular Fuzzy Biclosure spaces, Kathmandu University Journal of Science, Engineering and Technology, vol 8, no 8, pp 43-47.

Tripathi, R., Srivastava, M., Agrawal, A. K. (2017) A note on fuzzy continuous mappings in fuzzy biclosure spaces, Journal of ultra scientist of physical sciences, vol 29, no 12, pp 547-553.

Vadivel, A., Vijayalakshmi, R. and Krishnaswamy, D. (2010) B- generalized regular and B- generalized normal spaces, International Mathematical Forum, vol 5, no 54, pp 2699-2706.

Viriyapong, N., Srisarakham, E., Thongmoon, M. and Boonpok, C. (2012) g-Hausdorff and ∂- Hausdorff Fuzzy biclosure spaces, Applied Mathematical Sciences, vol 6, pp 6959-6970.

### Refbacks

- There are currently no refbacks.

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

CC BY-SA