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

Alexander J. Izzo

doi:10.7146/math.scand.a-23688

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

Authors

Alexander J. Izzo

DOI:

https://doi.org/10.7146/math.scand.a-23688

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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Published

2016-06-09

How to Cite

Izzo, A. J. (2016). Existence of Continuous Functions That Are One-to-One Almost Everywhere. MATHEMATICA SCANDINAVICA, 118(2), 269–276. https://doi.org/10.7146/math.scand.a-23688