Long line (topology)
Topological space in mathematics / From Wikipedia, the free encyclopedia
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In topology, the long line (or Alexandroff line) is a topological space somewhat similar to the real line, but in a certain way "longer". It behaves locally just like the real line, but has different large-scale properties (e.g., it is neither Lindelöf nor separable). Therefore, it serves as an important counterexample in topology.[1] Intuitively, the usual real-number line consists of a countable number of line segments laid end-to-end, whereas the long line is constructed from an uncountable number of such segments.