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Ultrafilter convergence in ordered topological spaces
We characterize ultrafilter convergence and ultrafilter compactness in
linearly ordered and generalized ordered topological spaces. In such spaces,
and for every ultrafilter , the notions of -compactness and of
-pseudocompactness are equivalent. Any product of initially
-compact generalized ordered topological spaces is still initially
-compact. On the other hand, preservation under products of certain
compactness properties are independent from the usual axioms for set theory.Comment: v. 2: some additions and some improvement
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