Show that $\left\{a_{n}:n\in\mathbb{N}\right\} \cup \left\{ a\right\}$ is closed
55614
Prove that a set consisting of a sequence and its limit point is closed
46240
Show that if $A$ and $B$ are sets, then $(A\cap B) \cup (A\cap \overline{B})=A$.
114608
Proof concerning regular space: there exist a closed set contained in any open set containing $x$
75604
Proof that $\partial(A\times B) = ((\partial A)\times B)\cup (A\times(\partial B))$
61930
Intersection of Closed and Compact Set is Closed
154076
How to show this property of $\mathbb{RP}^{n}$.
126821
Let $f:[0,1]\to \mathbb{R}$. Show that $\{a \in [0,1]: f(a)\neq 0\} = \bigcup_{n=1}^{\infty} \{a \in [0,1]: |f(a)|\geq 1/n\}$
46698
Showing a set is closed under inverses
99678
Is a sphere a closed set?
5132
Given $A\cap \overline{B}\neq \emptyset$, prove $A\cup B$ connected.
61670
Proving that $(b_n) \to b$ implies $\left(\frac{1}{b_n}\right) \to \frac{1}{b}$
101286
How show that $|a_{n}-1|\le c\lambda ^n,\lambda\in (0,1)$
22077
Closed form for the sequence defined by $a_0=1$ and $a_{n+1} = a_n + a_n^{-1}$
42494
The boundary is a closed set
13167
Prove $A = (A \setminus B) \cup (A \cap B)$
102170
Showing a Sequence and its Limit are Closed
92774
Prove that a linear subspace of $C([0,1])$ is closed