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 [pl] 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.