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
Abstract
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 T₁ 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.