Generalized open sets in grill N-topology

M. Lellis Thivagar; Ivan L. Reilly; M. Arockia Dasan; V. Ramesh

doi:10.4995/agt.2017.6797

Authors

M. Lellis Thivagar Madurai Kamaraj University
Ivan L. Reilly University of Auckland
M. Arockia Dasan Madurai Kamaraj University
V. Ramesh Madurai Kamaraj University

DOI:

https://doi.org/10.4995/agt.2017.6797

Keywords:

Grill N-topological space, GNτ -α open sets, GNτ -semi open sets, GNτ -pre open sets, GNτ -β open sets

Abstract

The aim of this paper is to give a systematic development of grill N-topological spaces and discuss a few properties of local function. We build a topology for the corresponding grill by using the local function. Furthermore, we investigate the properties of weak forms of open sets in the grill N-topological spaces and discuss the relationships between them.

Downloads

Download data is not yet available.

Author Biographies

M. Lellis Thivagar, Madurai Kamaraj University

Professor & Head School of Mathematics

Ivan L. Reilly, University of Auckland

Professor
Department of Mathematics

M. Arockia Dasan, Madurai Kamaraj University

Research Scholar
School of Mathematics

V. Ramesh, Madurai Kamaraj University

Research Scholar
School of Mathematics

References

A. Al-Omari and T. Noiri, Decompositions of continuity via grills, Jordan J. Math. Stat. 4, no. 1 (2011), 33-46.

D. Andrijevic, Semi-preopen sets, Mat. Vesnik. 38, no. 1(1986), 24-32.

K. C. Chattopadhyay, O. Njastad and W. J. Thron, Merotopic spaces and extensions of closure spaces, Can. J. Math. 35, no. 4 (1983), 613-629. https://doi.org/10.4153/CJM-1983-035-6

G. Choquet, Sur les notions de filter et grill, Comptes Rendus Acad. Sci. Paris. 224 (1947), 171-173.

H. Corson and E. Michael, Metrizability of certain countable unions, Illinois J. Math. 8 (1964), 351-360.

E. Hatir and S. Jafari, On some new classes of sets and a new decomposition of continuity via grills, J. Adv. Math. Studies. 3, no. 1 (2010), 33-40.

N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer Math. Monthly. 70 (1963), 36-41.

https://doi.org/10.2307/2312781

M. Lellis Thivagar, V. Ramesh and M. Arockia Dasan, On new structure of $N$-topology, Cogent Math. 3 (2016), 1204104, 10 pp.

A. S. Mashhour, I. A. Hasanien and S. N. El-Deeb, On pre continuous and weak pre continuous mappings, Proc. Math. Phys. Soc. Egypt. 53 (1982), 47-53.

A. S. Mashhour, I. A. Hasanien and S. N. El-Deeb, $alpha$-continuous and $alpha$-open mappings, Acta. Math. Hungar. 41, no. 3-4(1983), 213-218. https://doi.org/10.1007/BF01961309

O. Njastad, On some classes of nearly open sets, Pacific J.Math. 15 (1965), 961-970. https://doi.org/10.2140/pjm.1965.15.961

I. L Reilly and M. K. Vamanamurthy, On $alpha$-continuity in topological spaces, Acta Math. Hungar. 45 (1985), 27-32. https://doi.org/10.1007/BF01955019

B. Roy and M. N. Mukherjee, On a typical topology induced by a grill, Soochow J. Math. 33, no. 4 (2007), 771-786.