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. 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