This is a better forum for these sorts of questions:
Mathematics Stack Exchange
Polymath will have an answer, but your question is at the level of graduate level topology and does not really belong here. Some aspects of mathematics are pathological and do not have any physical basis in our Universe, maybe others, perhaps.
Mathematics Stack Exchange
Polymath will have an answer, but your question is at the level of graduate level topology and does not really belong here. Some aspects of mathematics are pathological and do not have any physical basis in our Universe, maybe others, perhaps.