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Existence of Continuous Functions That Are One-to-One Almost Everywhere

Alexander J. Izzo

Abstract


It is shown that given a metric space $X$ and a $\sigma$-finite positive regular Borel measure $\mu$ on $X$, there exists a bounded continuous real-valued function on $X$ that is one-to-one on the complement of a set of $\mu$ measure zero.

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DOI: http://dx.doi.org/10.7146/math.scand.a-23688

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ISSN 0025-5521 (print) ISSN 1903-1807 (online)

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