Coordinate functions of space filling curves. (English) Zbl 1018.26002

Summary: Given a continuous function \(X(t)\) mapping \([0,1]\) continuously onto \([0,1]\), several properties are given which this function must fulfill if there is to be another continuous function \(Y(t)\) so that \((X(t), Y(t))\) takes the unit interval onto the unit square.


26A27 Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives
54F45 Dimension theory in general topology