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Symbols for homeomorphic, isomorphic, homotopic

by quasar987
Tags: homeomorphic, homotopic, isomorphic, symbols
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quasar987
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Feb7-07, 12:25 AM
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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?
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dextercioby
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Feb7-07, 12:54 AM
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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].
matt grime
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Feb7-07, 04:35 AM
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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.

Crosson
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Feb7-07, 02:22 PM
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Symbols for homeomorphic, isomorphic, homotopic

I have never used a text in which the author used a symbol for these concepts without first defining it.
quasar987
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Feb7-07, 05:05 PM
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No doubt, but the question is: which symbol did they use for each concept?
Crosson
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Feb7-07, 07:09 PM
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Quote Quote by quasar987 View Post
No doubt, but the question is: which symbol did they use for each concept?
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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