# Symbols for homeomorphic, isomorphic, homotopic

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## Main Question or Discussion Point

My professor seems to randomly use the symbols $\approx$, $\cong$ and $\simeq$ to denote either homeomorphic, isomorphic or homotopic. So, what is the official symbol for each?

dextercioby
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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 $\simeq$.

matt grime
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Isomorphic is more frequently $\cong$, 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 $\sim$ a lot as well.

I have never used a text in which the author used a symbol for these concepts without first defining it.