Some results on mean open, closed and clopen sets

Year 2018, Volume: 47 Issue: 1, 101 - 106, 01.02.2018

Ajoy Mukharjee Kallol Bhandhu Bagchi

Abstract

In this paper, we obtain some more properties of mean open and closed sets. We also introduce a notion of mean clopen sets and obtain some
properties of such sets. We observe that a mean clopen set is both mean open and mean closed but the converse is not true.

Keywords

Maximal open set, Minimal open set, Mean open set, Mean closed set, Mean clopen set

References

• Mukharjee, A. On maximal and minimal clopen sets, An. Univ. Oradea Fasc. Mat. 23 (2), 127–130, 2016.
• Mukharjee, A. On maximal, minimal open and closed sets, Commun. Korean Math. Soc. 30 (3), 277–282, 2015.
• Mukharjee, A. and Bagchi, K.B. On mean open and closed sets, Kyungpook Math. J. 56 (4), 1259–1265, 2016.
• Nakaoka, F. and Oda, N. Minimal closed sets and maximal closed sets, Int. J. Math. Math. Sci. 2006, Article ID 18647, 8 pages.
• Nakaoka, F. and Oda, N. Some properties of maximal open sets, Int. J. Math. Math. Sci. (21), 1331–1340, 2003.
• Nakaoka, F. and Oda, N. Some applications of minimal open sets, Int. J. Math. Math. Sci. 27 (8), 471–476, 2001.