The {\em monotonicity} property of a space-filling curve stipulates 
that given the two points $x = {x_1, x_2, ..., x_d}$ and $y = {y_1, 
y_2, ..., y_d}$ such that $x_1 < y_1$, $x_2 < y_2$, ..., $x_d < y_d$ 
(i.e., $y$ is said to {\em dominate} $x$), then $x$ is always visited 
before $y$.  A space-filling curve is said to be {\em admissible} if 
at each position in the ordering at least one 4-adjacent neighbor in 
each of the lateral directions (i.e., horizontal and vertical) must 
have already been encountered. Can you show the equivalence of 
admissibility and monotonicity properties of space-filling curves?