Symbols for homeomorphic, isomorphic, homotopic

[quasar987]

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]

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]

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.

 

[Crosson]

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

 

[quasar987]

No doubt, but the question is: which symbol did they use for each concept?

 

[Crosson]

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.