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.
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
Section
Articles