Does $F$ is an isomorphism $\implies F^{-1}$ is an isomorphism?
88928
$F:G\to B$ is an isomorphism between groups implies $F^{-1}$ is an isomorphism
120811
What does "isomorphic" mean in linear algebra?
89190
Why is it true that $|AB:A|=|B:A\cap B|$ even if $A$ is not normal in $AB$? (Second Isomorphism Theorem)
121993
Prove that $f$ is one-to-one iff $f \circ h = f \circ k$ implies $h = k$.
119160
Isomorphism between complex numbers minus zero and unit circle
140503
What properties do natural isomorphisms between functors preserve?
110808
Isomorphisms preserve cyclic
121395
Let $X$ and $Y$ be non-empty sets and let $f:X \rightarrow Y$. Prove that $ f^{ −1} :P(Y ) → P(X) $ is injective if, and only if, $f$ is surjective.
13575
Need help for proving that: $f(f^{-1}(A)) ⊆ A$
40209
$f : S^1 \to\mathbb R$ is continuous then $f(x)=f(-x)$ for some $x\in S^1$
116594
Finite fields are isomorphic
111756
How do I prove that then $f(x) = 1$ for some $x ∈ [0, 1]$?
118354
Epimorphism and Monomorphism = Isomorphism?
23579
If $G$ is isomorphic to $H$, then ${\rm Aut}(G)$ is isomorphic to ${\rm Aut}(H)$
19346
Isomorphism of affine varieties
14994
Showing a function $f$ cannot be surjective
76610
Show that $f^{-1}(A \cup B) = f^{-1}(A) \cup f^{-1}(B)$