Show that $d_1=\min(d(x,y),2)$ is a metric space
42266
Show that $d(x,y)=\min \{1,|x-y|\}$ is a metric on $\mathbb R$
64260
Prove that a function between metric spaces is continuous iff the inverse image of a closed set is closed
69528
Metrizability of quotient spaces of metric spaces
123061
$X$ metric separable then $C(X)$ separable
151984
Proving the existence of a metric space
9775
Metric on Cartesian Product
132641
Proving that Euclidean Space is a complete metric space
158399
Show that $\{(x_1,x_2):x_1x_2\geq4,x_1>0,x_2>0\}$ is a convex set
133504
Suppose $X$ is a metric space and $S \subseteq X.$ Then, $S^o=\{x \in X~|~dist(x,S^c)>0\}$.
102485
Showing that a topological space is ${\rm T}_1$
3537
Show the Euclidean metric and maximum metric are strongly equivalent.
62479
A isometric map in metric space is surjective?
58329
Show that $y_1$ and $y_2$ are not Linearly Independent
146485
Prove that the product space is a metric space.
141529
Proving existence of a minimum
114047
Metric $d(x,y)=\frac{|x-y|}{\sqrt{1+x^2}\sqrt{1+y^2}}$ on $\mathbb{R}$
78733
Finding the density for $\min\{X, Y\}$