A characterization of monotonically Lindelof generalized ordered spaces

摘要

A space X is said to be monotonically Lindelof if for any open cover U of X, there exists a countable open cover rU such that rU refines V and if an open cover V of X refines U, then rU refines rU. Gruenhage shows that every Lindelof first-countable GO-space is monotonically Lindelof. In the paper we obtain the following result: A Lindelof GO-space X is monotonically Lindelof if and only if