any one / anyone
A single person or thing from a group versus the indefinite pronoun.
Write anyone as one word for “anybody”: Anyone can apply. Write any one as two words when one is a number you could point to: any one of the keys, any one candidate. If you can add single without wrecking the sense, you want two words.
Examples
UseAnyone who arrives late will wait.
UseAny one of these three proofs will do.
AvoidAny one who arrives late will wait.