A NOTE ON MONOTONICALLY STAR LINDELOF SPACES

A space X is mono tonically star Lindelof if one assign to for each open cover U a subspace s (U) subset of X, called a kernel, such that s (U) is a Lindelof subset of X, and st (s(U); U) = X, and if V refines U then s(U) subset of s(V), where s t (s (U); U) = U{U is an element of U : U boolean AND s(U) not equal empty set}. In this paper, we investigate the relationship between monotonically star Lindel of spaces and related spaces, and also study topological properties of monotonically star Lindelof spaces.