Proving the injectivity of function
9700
Consider the subset $B=\{(x,y):x^2+y^2\leq 1\}\ \subseteq \mathbb{R}^2$. Show that $\vert B \vert = \vert \mathbb{R}^2 \vert$.
74453
Injective and Surjective Functions
6023
Surjectivity of Composition of Surjective Functions
29154
$f$ is continuous and open implies $f$ injective
73338
Prove that the closure of complement, is the complement of the interior
145875
Inverse of a bijection f is equal to its derivative
113109
Showing that a map is bijective and finding its inverse
116732
Proving that a continuous map is surjective
115636
Show that $f$ is either injective or a constant function.
157925
How to prove that the implicit function theorem implies the inverse function theorem?
45792
Rigorous proof that surjectivity implies injectivity for finite sets
152438
Is the composition of two injective functions injective?
28798
Proving injection and surjection with functions $F:C^B\to C^A$, $F(f)=f\circ\varphi$, $\varphi: A\to B$
37058
Induced maps in homology are injective
34260
Injective function from $\mathbb{R}^2$ to $\mathbb{R}$?
87723
Show a holomorphic function on unit disc with with $|f'(z) - f'(0)| < |f'(0)|$ is injective
40566
Counting surjective functions