surjective function and identity
2072
Demonstrate that if $f$ is surjective then $X = f(f^{-1}(X))$
41359
Constructing a bijection
84114
Does there exist a surjective homomorphism from $(\mathbb R,+)$ to $(\mathbb Q,+)$ ?
146356
To prove two sets are isomorphic is it sufficient to find 2 injections or 2 surjections?
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.
110014
Right Inverse for Surjective Function
32340
Continuous bijections and their inverses
63146
Proof of properties of injective and surjective functions.
146188
Why does a proof of $\exists f: X\to Y$ injection $\iff \exists g: Y \to X$ surjection requires the axiom of choice?
53168
Surjective, Injective, Bijective Functions from $\mathbb Z$ to itself
16610
Surjectivity of a map from a space to itself
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.
116732
Proving that a continuous map is surjective
58642
If $g \circ f$ is the identity function, then which of $f$ and $g$ is onto and which is one-to-one?
134104
Is there a Cantor-Schroder-Bernstein statement about surjective maps?
90566
There exists surjections from A onto B and vice versa, and there is no bijection between the sets?
117793
Finding a function $\mathbb{N} \to \mathbb{N}$ that is surjective but not injective.