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.
Lipparini, P. (2015). Ultrafilter Convergence in Ordered Topological Spaces. ORDER [10.1007/s11083-015-9365-9].
Ultrafilter Convergence in Ordered Topological Spaces
LIPPARINI, PAOLO
2015
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.File in questo prodotto:
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A2GOuf.pdf
accesso aperto
Descrizione: preprint
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279.71 kB
Formato
Adobe PDF
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279.71 kB | Adobe PDF | Visualizza/Apri |
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