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Partial order and topology
Posted:
Sep 13, 2011 11:45 PM


I have only seen the order topology defined for a totally ordered set, but it can be defined for partial orders as well:
Let X be a partially ordered set. Define the order topology to be that generated by {{x in X: x < a}, {x in X: x > a}: a in X}.
Two questions:  If X and Y are partially ordered sets that are homeomorphic under order topologies, are X and Y necessarily orderisomorphic?  Is it true that any space can be given a partial order such that the topology is the order topology?
 Stephen J. Herschkorn sjherschko@netscape.net Math Tutor on the Internet and in Central New Jersey and New York



