No injection between the power set of a set A and the set A.
20706
Non-existence of a Surjective Function from a Set to Its Subsets (Cantor's theorem)
3896
A closed set in $(A, \mathcal T_A)$ that is not closed in $(X, \mathcal T)$
100726
Prove that the set of powers of a set, $\{ A^n : n \in \mathbb{N} \}$ exists by using ZFC axioms (without replacement).
39466
Multiplication operator has no no eigenvalues
71653
Why is the Cartesian product of a set $A$ and empty set an empty set?
158426
Proving lemma about centrality of idempotent elements in a Ring with no nilpotent elements.
19954
Perfect set without rational numbers
132382
Showing a set is nowhere dense in $C([0,1])$
146891
Why is $\{\emptyset\} \not = \emptyset$?
41997
Can the boundary of a set be ignored, when integrating over it.
99631
Prove/Disprove: Find $a\in S_4$ that is not a power of $b$ such that $ab=ba$ while $b=(123)$
136917
Torsion elements do not form a submodule.
40663
$a_1 a_1', a_2 a_2', ..., a_n a_n'$ is not a reduced modulo system $\mod p$.
125161
Why is the Cartesian product of $A$ and $\varnothing$ empty?
7622
$AB-BA=I$ having no solutions
88982
Prove that for any two sets $A$ and $B$, $A\notin B$ or $B\notin A$
143003
$\bigcup \emptyset$ is defined but $\bigcap \emptyset$ is not. Why?