Nikiel's conjecture

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. Nikiel, J. (1986). "Some problems on continuous images of compact ordered spaces". Questions and Answers in General Topology. 4: 117–128.
  2. Rudin, M.E. (2001). "Nikiel's Conjecture". Topology and Its Applications. 116: 305–331. doi:10.1016/S0166-8641(01)00218-8.


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