Symbols for homeomorphic, isomorphic, homotopic

1. Feb 7, 2007

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?

2. Feb 7, 2007

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 $\simeq$.

3. Feb 7, 2007

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.

4. Feb 7, 2007

Crosson

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

5. Feb 7, 2007

quasar987

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

6. Feb 7, 2007

Crosson

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.