COMPACTNESS AND REGULARITY VIA MAXIMAL OPEN AND MINIMAL CLOSED SETS IN TOPOLOGICAL SPACES

  • AJOY MUKHARJEE
    Department of Mathematics, St. Joseph's College, Darjeeling, W. Bengal- 734 104, INDIA.
  • SANTANU RAUT
    Department of Mathematics, Mathabhanga College, Mathabhanga, Coochbehar, W. Bengal- 736 146, INDI
  • KALLOL BHANDHU BAGCHI
    Department of Mathematics, Kalipada Ghosh Tarai Mahavidyalaya, Siliguri, W. Bengal- 734 014, INDIA.

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.

Cuvinte cheie

maximal open set minimal closed set maximal open cover m-compact space c-normal space