Answer:
This is both a mathematical and a philosophical question.
From a mathematical standpoint, it is possible to conceive of a dimension that is smaller than the three that we typically think of as 'space'. This is, in fact, one of the components of brane theory, a branch of higher-level mathematics which is attempting to come up with a unified theory of the universe.
From a philosophical angle, if there is space with nothing in it, and no one to observe it, does it really exist? This might be the modern equivalent of the 'if a tree falls when no one is there, does it still make a sound' argument which has baffled philosophers for centuries.