Counterexample to show that the interior of union may be larger than the union of interiors
24708
Why is $\operatorname{Int}(A) \cup \operatorname{Int}(B) \neq \operatorname{Int}(A \cup B)$?
63538
Impossibility of constructing a continuum-size linearly independent set in $\Bbb R$
127900
Interior of closure of open set in topological space
83778
An incorrect proof by exhaustion
95728
The union of growing circles is not homeomorphic to wedge sum of circles
81509
The cardinality of a countable union of countable sets, without the axiom of choice
94421
Why $P(A) \cup P(B)$ is not equivalent to $P(A \cup B)$
132532
Things around $(\forall x)(\Psi \Rightarrow \Phi) \Leftrightarrow ((\exists z)\Psi) \Rightarrow \Phi)$
126633
Is a contradiction enough to prove a set equality to $\varnothing$?
65888
A counterexample to theorem about orthogonal projection
39842
Limit point Compactness does not imply compactness counter-example
77297
Counterexample for $A,B\triangleleft G,G/A\cong B \Rightarrow G/B\cong A$
139988
Counter example for a result of intersection of subspaces
152382
Can an infinite set A be larger than an infinite set B but still have the same cardinality?
55564
Can the union axiom be weakened?
86325
Is an increasing union of subspaces a subspace?
153028
Showing that the product of vector magnitudes is larger than their dot product