Symbols for homeomorphic, isomorphic, homotopic

by quasar987
Tags: homeomorphic, homotopic, isomorphic, symbols
 Sci Advisor HW Helper PF Gold P: 4,771 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?
 Sci Advisor HW Helper P: 11,915 I don't think there's a universal convention for the first and the third, but in group theory "isomorphic to" is denoted by $\simeq$.
 Sci Advisor HW Helper P: 9,396 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.