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?

  • 2
    $\begingroup$ It denotes the restriction of a function to a subset of its domain. $\endgroup$ – Eike Schulte Mar 22 '17 at 21:16
  • $\begingroup$ Sometimes it is more usual to see it as $\;f\upharpoonright_\Phi\;$ , for example. $\endgroup$ – DonAntonio Mar 22 '17 at 21:43
  • $\begingroup$ Indeed, the notation I usually see for a restriction is $f|_\Phi$ $\endgroup$ – Luca S. Mar 23 '17 at 0:51

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.

  • $\begingroup$ I see, then it's a simpler concept than I thought. Thanks for the answer! $\endgroup$ – Luca S. Mar 22 '17 at 21:19

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