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arXiv:1508.03778 [math.GN]AbstractReferencesReviewsResources

Existence of continuous functions that are one-to-one almost everywhere

Alexander J. Izzo

Published 2015-08-15Version 1

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.

Categories: math.GN, math.PR
Subjects: 54C30, 26E99, 46E30, 54E40
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