Symbols for homeomorphic, isomorphic, homotopic

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The discussion highlights the lack of a universal convention for symbols representing homeomorphic, isomorphic, and homotopic relationships in mathematics. While \simeq is commonly used for isomorphic in group theory, \cong is also frequently seen for isomorphic relationships. The symbols \approx and \simeq are often used interchangeably for homeomorphic and homotopic, but their usage varies by author. Participants note that authors typically define their chosen symbols within their texts, leading to inconsistencies. Ultimately, the choice of symbols is subjective and depends on individual preferences.
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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?
 
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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.
 
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.
 
No doubt, but the question is: which symbol did they use for each concept?
 
quasar987 said:
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.
 

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