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.
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/03 - Geometria
Settore MAT/01 - Logica Matematica
English
Con Impact Factor ISI
Linearly ordered Generalized ordered topological space Ultrafilter convergence Compactness Pseudocompactness (pseudo-)gap Converging ν-sequence (weak) [ν, ν]-compactness (weak) initial λ-compactness Complete accumulation point λ-boundedness Decomposable Descendingly complete Regular ultrafilter
http://link.springer.com/article/10.1007/s11083-015-9365-9
Lipparini, P. (2015). Ultrafilter Convergence in Ordered Topological Spaces. ORDER [10.1007/s11083-015-9365-9].
Lipparini, P
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2108/134354
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