The difference between no one and no-one
TLDR: Depends on the context. Just read it.
These words are not always interchangeable, so take note.
no one (pronoun)—nobody; not one single person
No one was willing to put up their hand and volunteer to clean the whiteboard.
No one man should have such power.
‘I tell you, there’s no one in there!’
While the spelling noone is fairly frequently found online, this compound form of no one is not widely accepted as correct. However, no-one has been widely condoned as a way to reduce ambiguity between the uses of no one. It would be used thusly:
No-one was willing to put up their hand and volunteer to clean the whiteboard.
No one man should have such power.
‘I tell you, there’s no-one in there!’
Where people frequently trip up is, if they do use the hyphenated no-one, they often miss the instances where no one is the correct phrase to use, as in the second example ‘no one man should have such power’.
However, it is widely accepted to use no one in both situations as a spelling preference. So if you are of the hyphen persuasion and having a bit of trouble figuring out when to use the hyphen and when to leave it out, why not drop the hyphen altogether and be correct every time?