Notation: Why Ω for the based loop functor?

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?

• Wouldn't surprise me. Note also that $\Delta$ is used to denote the simplex category and objects therein, and $\Lambda$ a horn of a simplex. – Todd Trimble Apr 24 '17 at 10:52
• It would help if we knew who chose that notation, and when they 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 $\Omega S^{n+1}$. – Charles Rezk Apr 24 '17 at 14:31
• Of course, I should have checked Serre first: he uses $\Omega_x$ for "based loops of $X$ at $x$" in his 1951 Annals paper about the Serre spectral sequence, for instance. – Charles Rezk Apr 24 '17 at 14:37
• Morse's book "The Calculus of Variations in the Large" from 1934 uses $\Omega$ for the based loops in a manifold. – Mark Grant Apr 26 '17 at 19:39