Cantor Meanders

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}, $\cdots$ .

The space X has uncountably many arc components.

Cantor Meanders- fig. a


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