If $\forall \mathcal F(\bigcup \mathcal F = A \Rightarrow A \in \mathcal F)$ then A has exactly one element
86977
If $\cup \mathcal{F}=A$ then $A \in \mathcal{F}$. Prove that $A$ has exactly one element.
82597
How to find $ f(x)$ if $f(1-f(x))=x$ for all $x$ $\in \mathbb{R}$
84510
If $f(\mathbb{C})\subset \mathbb{C}-[0,1]$ then $f$ is constant
13575
Need help for proving that: $f(f^{-1}(A)) ⊆ A$
112049
How many elements does $\mathcal{P}(A)$ have?
70307
$(A\cap B)\cup C = A \cap (B\cup C)$ if and only if $C \subset A$
30694
Show that there exist $[a,b]\subset [0,1]$, such that $\int_{a}^{b}f(x)dx$ = $\int_{a}^{b}g(x)dx$ = $\frac{1}{2}$
22232
Proving that cardinality of the reals = cardinality of $[0,1]$
76285
Suppose $f$ is entire and $|f(z)| \leq 1/|Re z|^2$ for all $z$. Show that $f $ is identically $0$.
31522
Proving $f$ has at least one zero inside unit disk
17343
Function on $[a,b]$ that satisfies a Hölder condition of order $\alpha > 1 $ is constant
19146
Showing that $f$ has exactly one fixed point
155063
Is Cl(f(A)) a subset of f(Cl(A))?
122814
Finite Sets, Equal Cardinality, Injective $\iff$ Surjective.
33030
Proof that $\inf A = -\sup(-A)$
13162
Prove $\alpha \in R[[x]]$ is a unit iff $a_0 \in R$ is a unit
60707
Show that if $ \ A \cup B = A$ and $ \ A\cap B = A$ then $ \ A = B$