Symbols for homeomorphic, isomorphic, homotopic


by quasar987
Tags: homeomorphic, homotopic, isomorphic, symbols
quasar987
quasar987 is offline
#1
Feb7-07, 12:25 AM
Sci Advisor
HW Helper
PF Gold
quasar987's Avatar
P: 4,768
My professor seems to randomly use the symbols [itex]\approx[/itex], [itex]\cong[/itex] and [itex]\simeq[/itex] to denote either homeomorphic, isomorphic or homotopic. So, what is the official symbol for each?
Phys.Org News Partner Mathematics news on Phys.org
Math modeling handbook now available
Hyperbolic homogeneous polynomials, oh my!
Researchers help Boston Marathon organizers plan for 2014 race
dextercioby
dextercioby is offline
#2
Feb7-07, 12:54 AM
Sci Advisor
HW Helper
P: 11,866
I don't think there's a universal convention for the first and the third, but in group theory "isomorphic to" is denoted by [itex] \simeq [/itex].
matt grime
matt grime is offline
#3
Feb7-07, 04:35 AM
Sci Advisor
HW Helper
P: 9,398
Isomorphic is more frequently [itex]\cong[/itex], 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 [itex]\sim[/itex] a lot as well.

Crosson
Crosson is offline
#4
Feb7-07, 02:22 PM
P: 1,294

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.
quasar987
quasar987 is offline
#5
Feb7-07, 05:05 PM
Sci Advisor
HW Helper
PF Gold
quasar987's Avatar
P: 4,768
No doubt, but the question is: which symbol did they use for each concept?
Crosson
Crosson is offline
#6
Feb7-07, 07:09 PM
P: 1,294
Quote Quote by quasar987 View Post
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.


Register to reply

Related Discussions
The set {A in GL(n;R) | det(A)>0} is homeomorphic to the set {A in GL(n;R) | det(A)<0 Differential Geometry 4
[SOLVED] homotopic curves Calculus & Beyond Homework 7
Is Q Homeomorphic to N? Calculus 3
Homotopic Funtor Linear & Abstract Algebra 2
Question about how to use Homotopic Curves. Calculus 2