Abstract:We characterize ultrafilter convergence and ultrafilter compactness in linearly ordered and generalized ordered topological spaces. In such spaces, and for every ultrafilter D, the notions of D-compactness and of D-pseudocompactness are equivalent. Any product of initially λ-compact generalized ordered topological spaces is still initially λ-compact. On the other hand, preservation under products of certain compactness properties is independent from the usual axioms for set theory
Set email alert for when this publication receives citations?
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.