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Nikiel's conjecture

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In mathematics, Nikiel's conjecture in general topology was a conjectural characterization of the continuous image of a compact total order. The conjecture was first formulated by Jacek Nikiel in 1986[1]. The conjecture was proven by Mary Ellen Rudin in 1999[2].

The conjecture states that a compact topological space is the continuous image of a total order if and only if it is a monotonically normal space.

Notes

  1. ^ J. Nikiel, Some problems on continuous images of compact ordered spaces, Questions Answers Gen. Topology 4 (1986), 117–128
  2. ^ M.E. Rudin, "Nikiel's Conjecture" Topol. Appl. 116 (2001) 305–331
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