Ultrafilter Convergence in Ordered Topological Spaces

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• 作者：Paolo Lipparini
• 刊名：Order
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：33
• 期：2
• 页码：269-287
• 全文大小：334 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Convex and Discrete Geometry
  Geometry
  Theory of Computation
  
• 出版者：Springer Netherlands
• ISSN：1572-9273
• 卷排序：33

文摘

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.KeywordsLinearly orderedGeneralized ordered topological spaceUltrafilter convergenceCompactnessPseudocompactness(pseudo-)gapConverging ν-sequence(weak) [ν, ν]-compactness(weak) initial λ-compactnessComplete accumulation pointλ-boundednessDecomposableDescendingly completeRegular ultrafilter