# Subtile finesse de la notation…

For a long time (since I first heard of it around 1990), I thought that the terminology “Property (T)” was a completely arbitrary name, and no better than the thousand notions of “admissible thingummy” or “good khraboute” which sprinkle too many mathematics papers. Then I learnt a few years ago that the “T” was supposed to refer to the Ttrivial representation, since — in a suitable language — the property is about the trivial representation of a group $G$.

This was already better. But much more recently, I learnt from S. Mozes that the typography “(T)” itself was not some random choice, but was meant to express the fact that the trivial representation $T$ is supposed to be alone in some open set, incarnated as an open interval (so one should read $()$ as in $(a,b)$)…

A direct corollary is that the right translation in French is, of course, Property $]T[$.

By the way, I personally much prefer the $]a,b[$, $[a,b]$, $]a,b]$, etc, notation for intervals, but I’m told that many find this ugly beyond belief and much prefer the $(a,b)$, $(a,b]$, etc, style…