While phrases like no body, some body, and some one have evolved into the compound words nobody, somebody, and someone, the similar phrase no one has never gone this route. A quick internet search reveals that noone is surprisingly common, but the two-word form and the hyphenated form (no-one) remain far more common in books and in edited publications.
The hyphenated form, no-one, is especially common outside North America—it is almost completely absent from 21st -century U.S. and Canadian writing—but the unhyphenated form prevails everywhere by a significant margin. This is the case despite the fact that many English reference sources list the hyphenated form as the standard spelling or recommend it above the alternatives.
No one on board was seriously hurt, but authorities were concerned about the wellbeing of the whale. [Sydney Morning Herald]
It’s a sad thing when no one loves you, most of all if you are a new vehicle being shunned by the buying public. [Globe and Mail]
But the fact that these companies lack an IT department does not mean there is no one looking after technology. [Financial Times]
President Obama meets with Senate leaders, but no one wants to back away from tough stances on taxes. [Los Angeles Times]