Symbols for homeomorphic, isomorphic, homotopic

  1. quasar987

    quasar987 4,774
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    My professor seems to randomly use the symbols [itex]\approx[/itex], [itex]\cong[/itex] and [itex]\simeq[/itex] to denote either homeomorphic, isomorphic or homotopic. So, what is the official symbol for each?
     
  2. jcsd
  3. dextercioby

    dextercioby 12,324
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    I don't think there's a universal convention for the first and the third, but in group theory "isomorphic to" is denoted by [itex] \simeq [/itex].
     
  4. matt grime

    matt grime 9,395
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    Isomorphic is more frequently [itex]\cong[/itex], though the latex tag for it is cong. The symbol Dexter gave is actually in my experience likely to beused for homotopic, though I also see [itex]\sim[/itex] a lot as well.
     
  5. I have never used a text in which the author used a symbol for these concepts without first defining it.
     
  6. quasar987

    quasar987 4,774
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    No doubt, but the question is: which symbol did they use for each concept?
     
  7. That's what my post was meant to convey: there is no standard convention and so each author sets up his text to so that the symbol he likes most is used most frequently.
     
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