Monotonically star compact spaces

A space X is monotonically star-compact if one can assign to for each open cover U a subspace s(U) subset of X, called a kernel, such that s(U) is a compact subset of X, and st(s(U),U) = X, and if V refines U then s(U) subset of s(V), where st(s(U),U) = (MU is an element of U:U boolean AND s(U) not equal theta. In this paper, we investigate topological properties of monotonically star-compact spaces. (C) 2015 Elsevier B.V. All rights reserved.