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.

Downloads

Published

2016-06-09

Issue

Vol. 118 No. 2 (2016)

Section

Articles

How to Cite

[1]
A. J. Izzo, “Existence of Continuous Functions That Are One-to-One Almost Everywhere”, Math. Scand., vol. 118, no. 2, pp. 269–276, Jun. 2016, doi: 10.7146/math.scand.a-23688.