# Symbols for homeomorphic, isomorphic, homotopic

by quasar987
Tags: homeomorphic, homotopic, isomorphic, symbols
 PF Patron HW Helper Sci Advisor P: 4,755 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?
 HW Helper Sci Advisor P: 11,723 I don't think there's a universal convention for the first and the third, but in group theory "isomorphic to" is denoted by $\simeq$.
 HW Helper Sci Advisor P: 9,395 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.
P: 1,295

## 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.
 PF Patron HW Helper Sci Advisor P: 4,755 No doubt, but the question is: which symbol did they use for each concept?
P: 1,295
 Quote by quasar987 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.

 Related Discussions Differential Geometry 4 Calculus & Beyond Homework 7 Calculus 3 Linear & Abstract Algebra 2 Calculus 2