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.
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Lipparini, P. Ultrafilter Convergence in Ordered Topological Spaces. Order 33, 269–287 (2016). https://doi.org/10.1007/s11083-015-9365-9
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DOI: https://doi.org/10.1007/s11083-015-9365-9