Ultrafilter Convergence in Ordered Topological Spaces

摘要

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 lambda-compact generalized ordered topological spaces is still initially lambda-compact. On the other hand, preservation under products of certain compactness properties is independent from the usual axioms for set theory.