Suppose that (X, d) is complete and that A is a closed subset. Show A must be complete
13848
Showing that if a subset of a complete metric space is closed, it is also complete
128894
About compactness and completeness of set $X = \mathbb{R}$ with the metric $d(x, y) = \frac{|x-y|}{1+|x-y|}$
99341
Basic question: closure of irreducible sets
74312
If Y is complete then B(X,Y) is complete
79697
If $A$ is a subset of $B$, then the closure of $A$ is contained in the closure of $B$.
66293
$der(\{x\})$ is closed and $x\in der(der(A))$
61202
Show that $C[a,b]$ is a complete space under the metric $d(f,g)=\sup_{t\in [a,b]}|f(t)-g(t)|$.
28683
Sum of two closed sets in $\mathbb R$ is closed?
16060
Showing this metric space is complete
150011
Proof completeness of $(X,d)$ given $d$ is French railway metric
95887
How to show that quotient space $X/Y$ is complete when $X$ is Banach space, and $Y$ is a closed subspace of $X$?
32534
Prove that a set $S \subseteq \mathbb{R}$ is closed and bounded if and only if every sequence in $S$ has a sub sequence converging to a point of $S$.
40162
Prove that the set $\mathbb{Q}[\alpha] = \{a+b\alpha+c\alpha^2 \mid a, b, c \in\mathbb{Q}\}$ is closed under addition and multiplication.
146364
$X$ is connected iff $\forall A\subset X,$ $\partial A\neq\emptyset$
47680
Prove that the union of the interior of a set and the boundary of the set is the closure of the set
91991
How do I prove that two closed sets are separable?
149820
How do you prove the set $G = \{(x, f(x)) \mid x \in \mathbb R\}$ is closed?