if you never define and closed arena, does infinite space exist? For example lets say it was a square map

yes it does.
Have you tried driving your lightcycle into infinite space?
Oooh, it's scary.

but one can't always go through infinite space.

There's some info on the wiki on this, too lazy to dig it out. Basically at some distance from the bounding rectangle of all rim walls all cycles stop without using rubber or dieing, and if they somehow get further than that (spawns, for example) they immediately die.

You can simulate infinite space by putting two little walls at opposite edges of the map, far away from the spawn points. The floor will get messed up, though…