demonstrate that if X is a connected metric space, then X is chained.
107701
Show that a connected metric space is $\epsilon$-chainable for $\epsilon>0$
69777
Show that, for every metric $d$, the metrics $d/(1+d)$ and $\min\{1,d\}$ are equivalent
115695
If $X$ is a connected subset of a connected space $M$ then the complement of a component of $M \setminus X$ is connected
83159
Defining a metric space
51227
Proving that given metric space is complete: $X := (0,\infty)$ and $d:=|\ln(x)-\ln(y)|$
151984
Proving the existence of a metric space
85242
Deciding whether two metrics are topologically equivalent in the space $C^1([0,1])$
42266
Show that $d(x,y)=\min \{1,|x-y|\}$ is a metric on $\mathbb R$
82333
let $(X,d)$ be a metric space. How I can show that any finite subset of $X$ is closed.
147961
Characterizing simply connected spaces
93623
Showing that every connected open set in a locally path connected space is path connected
66550
Cardinality of separable metric spaces
9355
If $d(x,y)$ is a metric, then $\frac{d(x,y)}{1 + d(x,y)}$ is also a metric
39746
How to prove that given set is a connected subset of the space of matrices?
112303
Distances between closed sets on metric spaces
17067
To prove that $(\mathbb{P(N)},d)$ is a metric space
84791
Is every connected metric space with at least two points uncountable?