Stating whether a space is complete
132491
How to show that $C=C[0,1]$ is a Banach space
3148
True or false: {{∅}} ⊂ {∅,{∅}}
52014
Showing $(C[0,1], d_1)$ is not a complete metric space
73353
Is it true that a subset that is closed in a closed subspace of a topological space is closed in the whole space?
13848
Showing that if a subset of a complete metric space is closed, it is also complete
82333
let $(X,d)$ be a metric space. How I can show that any finite subset of $X$ is closed.
151984
Proving the existence of a metric space
49374
Closure of a subset in a metric space
97951
Is the void set (∅) a proper subset of every set?
27708
Are commands complete sentences?
119105
If $(X,d)$ is a complete metric space and $A$ is closed then show that for $x \in X$ there exists an element $a_0 \in A$ such that $d(x,A)=d(x,a_0)$
153945
When does blank space count?
8414
Proof verification: Set of partial limits of a sequence is closed
100362
Codomain of function complete implies function space complete
481
Can compact sets completey determine a topology?
50677
Is this metric space incomplete?
44457
Why we define the completeness of a space by the converge of a Cauchy sequence rather than a normal sequence?