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

Alexander J. Izzo

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arXiv · 1508.03778

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

Alexander J. Izzo

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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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Alexander J. Izzo. 2015-08-15. Existence of continuous functions that are one-to-one almost everywhere. https://arxiv.org/abs/1508.03778

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