The universal plane curve described by Sierpinski [1] in 1916 has proven highly useful in the development of various phases of topology and analysis which have gone ahead at such a rapid pace in the intervening period of over forty years. Interest in this curve and its analog in 3-space is currently much alive and its role in mathematics is surely by no means finished. The curve is obtained very simply as the residual set remaining when one begins with a square and applies the operation of dividing it into nine equal squares and omitting the interior of the center one, then repeats this operation on each of the surviving 8 squares, then repeats again on the surviving 64 squares, and so on indefinitely. Sierpinski showed that this set contains a topological image of every plane continuum having no interior point and thus it has come to be known as the Sierpinski plane universal curve.
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