Every open ball in a metric space is an open set.
101504
An open ball is an open set
62034
If every open set of a metric space $(X, \rho)$ is $\mu^*$-measurable, then $\mu^*$ is a metric outer measure.
123061
$X$ metric separable then $C(X)$ separable
36566
Equivalence classes and metric spaces
82333
let $(X,d)$ be a metric space. How I can show that any finite subset of $X$ is closed.
125580
Proving that every countable metric space is disconnected?
127900
Interior of closure of open set in topological space
107160
Open Set and Measure Theory
80860
How to call a space in which every G$_\kappa$-set is open
98553
Infinite metric space has open set $U$ which is infinite and its complement is infinite
49374
Closure of a subset in a metric space
151984
Proving the existence of a metric space
128730
Open subspaces of locally compact Hausdorff spaces are locally compact
59424
Showing that $B=\{(x,y) \in \Bbb{R^2} \mid \ xy>0 \}$ is an open set
93623
Showing that every connected open set in a locally path connected space is path connected
144353
A closed ball in a metric space is closed
49721
Prove the empty set is closed for a metric space (X,d).