Nikiel's conjecture explained

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 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 and Answers in General Topology. 4. 1986. 117–128.
2. M.E. . Rudin . Mary Ellen Rudin. Nikiel's Conjecture. Topology and Its Applications. 116. 2001. 305–331. 10.1016/S0166-8641(01)00218-8 . free.