Closure systems

This paper is concerned with the concept of closure. It is a notion which is found abundantly in most areas of mathematics. The generalized definition of "closure operation" is due to E. H. Moore in 1910. (Birkhoff, Lattice Theory, Pp. 49-51, 273.) The concept has received little attention in its general form. Since this concept has not been treated much in recent literature, the most basic properties of closure have been developed in Chapter II with great detail. The results of this study are given in Chapter III, with the main theorems being Theorem 6, 10 and 16.