CHARACTERIZING THE COORDINATE FUNCTIONS OF SPACE FILLING CURVES

摘要

The coordinate functions, / and g, of a space filling curve are continuous functions from [0,1] to [0,1] so that F(t) = (f(t),g(t)) maps [0,1] onto the unit square. In the paper Coordinate Functions of Space Filling Curves written by Foran, several necessary conditions for a continuous function / are given for there to be a continuous g so that F(t) = (f(t),g(t)) maps [0,1] onto [0,1]~2. In this paper, we define a new condition for / that is both necessary and sufficient to assure that f has a matching coordinate function g such that F(t) = (f(t),g(t)) filling the square.