Prove that a function $f$ is injective if and only if it respects intersection.
65977
Showing function is injective iff $f(M_1 \cap M_2) = f(M_1)\cap f(M_2)$
56413
$f(g(x))=g(f(x))$ implies $f(c)=g(c)$ for some $c$
65946
A function $f: \mathbb R \to \mathbb R$ satisfies equation $f(x+y)=f(x)f(y)$ for all $x,y\in \mathbb R $
71857
Proving that, $|f'(x)-f'(y)|\le k|x-y| \implies (f'(x))^2< 2 kf(x) $
48765
Let $S$ and $T$ be finite non-empty sets such that $|S| = |T|$. Show that the function $f : S\to T$ is onto if and only if it is one-to-one.
50966
In a topological space, why the intersection only has to be finite?
77944
Injective functions with intermediate-value property are continuous. Better proof?
84301
Showing that some Function on the Unit Disc is injective
62709
Functions that are sets of all function - proofs
76148
Show that $\exists c \in \mathbb{R} : f(c) = 0$
105455
Prove that "injective function $f:X\to Y$ exists" and "surjective function $g:Y\to X$ exists" is logically equivalent.
23125
Prove that there is a bijection between the set of all subsets of $X$, $P(X)$, and the set of functions from $X$ to $\{0,1\}$.
37308
Let $f:K\to K$ with $\|f(x)-f(y)\|\geq ||x-y||$ for all $x,y$. Show that equality holds and that $f$ is surjective.
20303
A function $f\colon E\to F$ between finite sets is injective iff it is surjective iff it is bijective
40609
Prove that $f(X)$ and $g(Y)$ are independent if $X$ and $Y$ are independent
63146
Proof of properties of injective and surjective functions.
55492
Existence of $f'\in F$ such that $f^{[G:F]}=(f')^n$ for finite extension $F\subset G$