To find an example for which $closure(\cup A_\alpha)\ne\cup closure(A_\alpha)$
64871
Closure of Union contains Union of Closures
97772
An example of a function which satisfies $\sup_{y}\inf_{x}f(x,y)<\inf_{x}\sup_{y}f(x,y)$
122086
continuous function: preimage of closure of a set is closure of preimage
26302
Prove that $(X \cap Y) \cup Z = (X \cup Z) \cap (Y \cup Z)$
37654
Topology: Example of a compact set but its closure not compact
30231
The boundary of union is the union of boundaries when the sets have disjoint closures
144383
The closure of a connected set in a topological space is connected
142168
can we a prove ⊢ (α → α) → (α → α)
145058
Prove $ (A \cup B) \cap C$ = $(A \cap C) \cup (B \cap C) $
65196
Gluing Lemma for Closed Sets: Infinite Cover Counter-Example
32910
Completion and algebraic closure commutable
109229
An Example of a Nested Decreasing Sequence of Bounded Closed Sets with Empty Intersection
68918
Show that $A\cap B\subseteq A$ and $A\subseteq A\cup B$
154363
Prove that $\text{aff}(X) = \text{aff}(\text{closure}(X))$
107281
Proof of Existence of Algebraic Closure: Too simple to be true?
123890
Show $A\setminus (A\cap B)=(A\cup B)\setminus B$
115606
Proofs involving $ (A\setminus B) \cup (A \cap B)$