Can someone go to the space without suit

The short answer, no. The long answer, space suits dont just protect the astronauts from the lack of oxygen but also the environment around them. Space is a vacuum & as such, excruciatingly cold & with the lack of atmosphere, crushing too.

Essentially if you stepped out of a space station with, say, a diving suit on, while youd have the air to breathe, your body would long freeze (or even worse, you might boil from the inside as your bodys crushed the due to pressure......or something like that anyways.....