Uniformization (set theory)

In set theory, the axiom of uniformization, a weak form of the axiom of choice, states that if ${\displaystyle R}$ is a subset of ${\displaystyle X\times Y}$, where ${\displaystyle X}$ and ${\displaystyle Y}$ are Polish spaces, then there is a subset ${\displaystyle f}$ of ${\displaystyle R}$ that is a partial function from ${\displaystyle X}$ to ${\displaystyle Y}$, and whose domain (in the sense of the set of all ${\displaystyle x}$ such that ${\displaystyle f(x)}$ exists) equals

...
Wikipedia