Unique Nearness Structures

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• 作者：H. L. Bentley ; H. Herrlich
• 关键词：Nearness space ; Symmetric topological space ; T1 topological space ; T2 topological space ; Indiscrete topology ; Cofinite topology ; One ; point compactification
• 刊名：Applied Categorical Structures
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：24
• 期：5
• 页码：439-445
• 全文大小：169 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematical Logic and Foundations
  Theory of Computation
  Convex and Discrete Geometry
  Geometry
  
• 出版者：Springer Netherlands
• ISSN：1572-9095
• 卷排序：24

文摘

We investigate which symmetric topological spaces have precisely one compatible nearness structure. We show how this situation exists for T₁ topological spaces and for T₂ topological spaces. The compatible nearness structures on a symmetric topological space form a sort of “interval” of structures with the topology itself as the topmost.