I am studying a paper about Subgroups of Infinite Symmetric Groups by Macpherson and Neumann; throughout the paper, the authors use the notation $\upharpoonright$.
For example, when they seek to topologize an infinite symmetric group $Sym(\Omega)$, they define the closure of a subset $X$ of $Sym(\Omega)$ as such:
$\{f \in Sym(\Omega) \ |$ for all finite subsets $\Phi$ of $\Omega$ there exists $x \in X$ such that $x\upharpoonright\Phi=f\upharpoonright\Phi\}$
The authors don't define this notation, but they use it in several proofs. What do the authors mean when they use it?
Best Answer
It is the truncation of a function to a particular set. That is, the subset of the function that has first-entries from the particular set.