Long Line (topology)
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. Therefore it serves as one of the basic counterexamples of topology. Intuitively, the usual real-number line consists of a countable number of line segments [0, 1) laid end-to-end, whereas the long line is constructed from an uncountable number of such segments.
Read more about Long Line (topology): Definition, Properties, p-adic Analog
Famous quotes containing the words long and/or line:
“I never had but one intrigue yet: but I confess I long to have another. Pray heaven it end as the first did tho’, that we may both grow weary at a time; for ‘tis a melancholy thing for lovers to outlive one another.”
—John Vanbrugh (1663–1726)
“Any walk through a park that runs between a double line of mangy trees and passes brazenly by the ladies’ toilet is invariably known as “Lover’s Lane.””
—F. Scott Fitzgerald (1896–1940)