This is just a question about notation - probably useless, but it's always baffled me:

*Why was $\Omega$ chosen to denote the based loop functor?*

I once heard someone speculate: "It's because $\Omega$ looks like... *a loop*?"

Is it really as simple as that? (If so, clever!) Can anyone verify and/or know more?

Thanks in advance!

(PS. I originally asked this question on StackExchange, but it seems Overflow is a better fit.)

whochose that notation, andwhenthey did. I don't know the answer. After poking around on MathSciNet, the earliest use of $\Omega$ for a loop space I can come up with is (MR0055683) G. Whitehead, "On the Freudenthal theorems" (Annals, 1953). He actually uses "$\Omega^{n+1}$" for what we call $\Omega S^{n+1}$. $\endgroup$ – Charles Rezk Apr 24 '17 at 14:31