The Cantor Meanders X is formed by combining the
product C x I of the Cantor Ternary Set C and
the unit interval I with the appropriate segments of
I x {0,1}. We use the 'zig-zag' system of selecting
the intervals. We start with
[1/3,2/3] x {0},
continue with
[1/9,2/9] x {1} and
[7/9,8/9] x
{1},
.
The space X has uncountably many arc components.