COMPACTNESS AND REGULARITY VIA MAXIMAL OPEN AND MINIMAL CLOSED SETS IN TOPOLOGICAL SPACES
AJOY MUKHARJEE 1, SANTANU RAUT 2 AND KALLOL BHANDHU BAGCHI 3 1. Department of Mathematics, St. Joseph's College, Darjeeling, W. Bengal- 734 104, INDIA.
e-mail: ajoyjee@gmail.com
2. Department of Mathematics, Mathabhanga College, Mathabhanga, Coochbehar, W. Bengal- 736 146, INDIA
e-mail: raut_santanu@yahoo.com
3. Department of Mathematics, Kalipada Ghosh Tarai Mahavidyalaya, Siliguri, W. Bengal- 734 014, INDIA.
e-mail: kbagchi.789@gmail.com
In this paper, we introduce and study the notion of maximal open cover which in turn leads us to define and study m-compact spaces. We prove that there always exists a maximal open cover in an infinite Tâ topological space. We also obtain some results on minimal c-regular and minimal c-normal spaces. We prove that a Hausdorff m-compact topological space is minimal c-normal.
