Ultrafilter convergence in ordered topological spaces

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

v. 2: some additions and some improvements

References in corpus (4)

• More generalizations of pseudocompactness
• Topological spaces compact with respect to a set of filters
• More Results on Regular Ultrafilters in ZFC
• Every weakly initially m-compact topological space is mpcap