Reason to Impeach Your Math Club President #17

1. 

   Mike

   February 27, 2012 at 10:41 pm

   They also said “isomorphic” when they meant “homeomorphic.”
   1. 

      Joshua

      March 6, 2012 at 2:03 pm

      A homeomorphism is an isomorphism in the category of topological spaces. So saying that they are topologically isomorphic is correct. The terminology just isn’t exactly standard.
      1. 

         Mike

         March 7, 2012 at 6:13 pm

         I would have to disagree. Isomorphisms inherently have to do with algebraic structure. “Topologically Isomorphic” would imply that they have an isomorphic algebraic structure- namely, fundamental group (If there’s another inherent algebraic structure on topological spaces, I don’t know about them. Not saying they don’t exist, though). However, spaces with isomorphic fundamental groups are not necessarily isomorphic (The sphere and R2 have trivial fundamental group, but are not homeomorphic, for instance)

         Maybe it’s not strictly speaking incorrect, but I don’t think there’s anyone who would actually say 2 topological spaces are isomorphic
2. 

   Michael

   February 28, 2012 at 7:14 am

   No fail here. Kevin was making a joke. @Dread Pirate Loki…. social fail!

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