Cratylus
Junior Member
- Joined
- Aug 14, 2020
- Messages
- 82
Let E and F be partially ordered classes, and let
g : E → F be an isomorphism. Prove that for
[MATH] x \in E[/MATH] g(Sx)=Sg(x)
conclude that Sx [MATH]\cong[/MATH] Sg(x).
questions
The question is assuming I showed each
function is an isomorphism, can I infer
equality ? If not, how about comparing
dom(g) and ran(g) of each function,
I have proved it by set inclusion but am not
happy with I t.
g : E → F be an isomorphism. Prove that for
[MATH] x \in E[/MATH] g(Sx)=Sg(x)
conclude that Sx [MATH]\cong[/MATH] Sg(x).
questions
The question is assuming I showed each
function is an isomorphism, can I infer
equality ? If not, how about comparing
dom(g) and ran(g) of each function,
I have proved it by set inclusion but am not
happy with I t.