Prop: If two functions $f,g$ are bijective, their compositions are also bijective.
96202
Prove composition of bijections is bijection
88201
Suppose $X$ is a finite set and $f : X \to X$ is a function. Then $f$ is injective if and only if $f$ is surjective.
141225
Number of all bijective functions from A to A.
57269
A special bijection between $\mathbb{R}\times \mathbb{R}$ and $\mathbb{R}$
7858
Proving that $f(x)$ is irreducible over $F(b)$ if and only if $g(x)$ is irreducible over $F(a)$
10850
Are all functions that have an inverse bijective functions?
133498
Show that Function Compositions Are Associative
46748
If $g \circ f$ is surjective, show that $f$ does not have to be surjective?
153634
A statment about the equivalence between the Axiom of Choice and the surjectivity of the projections.
28798
Proving injection and surjection with functions $F:C^B\to C^A$, $F(f)=f\circ\varphi$, $\varphi: A\to B$
95086
Homeomorphism is bijective
93964
Proving that $f$ is a bijection from $N$x$N$ to $N$.
107659
Let $f:A \to B$ and $g:B\to A$ be arbitrary functions.
973
Is the property "being a derivative" preserved under multiplication and composition?
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.
133699
Proving that there is a bijection between $A$ and $B$.
21707
Constructing a Bijective function via an injective and surjective one.