what the univers is expanding into is always under research. the shitty thing is that we just do not know yet right? we are at the mercy of thoeretical physics to explain something that we will never be able to tangibly experiment on. all the theories and hypothesis will never get us to where the universe is actually expanding so we can see for ourselves. the best we can hope for is that our theories will fit into the laws that we have conluded so far. we can call it space or we can come up with a new word to call it, the fact is we do not know and the reality is that we probably never will. we will just have to be content with theorists until then.
i agree with the statement that if space is infinite it has to encompass more than our finite universe.
are you familiar with the bubble theory? it says that our universe may be one in a sea of others. our universe could be right up against another just like bubbles in a bathtub. this still gives room for expansion too. any thoughts?