By ‘space’, I suppose you mean the Universe? It appears to be expanding at an ever increasing rate but it is not expanding into an empty space, it is expanding into nothing, I guess that means that as the Universe expands it is actually creating space! I believe that we exist in a multi dimensional multiverse and because we are in a three dimensional state, we just cannot comprehend what an existence in more than those three dimensions. So, I suppose that you can argue that the Universe (ours) is not infinite, it has its ‘edge’, in every direction, but that edge is expanding at an ever increasing rate.

Time is something that fascinates me; our concept and measurement of time is based on observers noting how often our planet orbits the Sun and its rotation. That would seem to be quite amazing if that explained the entire nature of time throughout the Universe! Think about it, what is the smallest period of time? How short can that period of time be? Infinitely small? That is quite a concept to wrap your thoughts around!