On every metric space $(T, d)$ metric $d:T^2 \to \mathbb{R}$ is continuous function?
4538
Is the mapping $ d : X\times X \mapsto \mathbb {R} $ continuous?
115794
When is the vector space of continuous functions on a compact Hausdorff space finite dimensional?
119247
Let $(M,d)$ be a compact metric space and $f:M \to M$ such that $d(f(x),f(y)) \ge d(x,y) , \forall x,y \in M$ , then $f$ is isometry?
35291
How to show $d(x,y)= \sqrt{d_1(x_1,y_1)^2+d_2(x_2,y_2)^2}$ is a metric?
63598
Is every separately continuous function on $R^2$ continuous?
51227
Proving that given metric space is complete: $X := (0,\infty)$ and $d:=|\ln(x)-\ln(y)|$
102075
A function continuous on all irrational points
33114
Uniqueness of a continuous extension of a function into a Hausdorff space
15487
Continuous function from a connected set?
38584
$T\colon L^2[0,1] \to L^2[0,1]$ be a bounded linear map of Hilbert spaces such that if $f\in L^2[0,1]$ is continuous then so is $Tf$.
34344
Is a function that maps every compact set to a compact set continuous?
2198
Maps from subsets of $\mathbb{R}^2$ that are either open/closed/continuous
24914
Does every continuous map from $\mathbb{Q}$ to $\mathbb{Q}$ extends continuously as a map from $\mathbb{R}$ to $\mathbb{R}$?
158221
Prob. 4 (a), Sec. 20 in Munkres' Topology, 2nd ed: Are these functions continuous in the product, uniform, and box topologies?
124535
continuous function from $[\pi,2\pi]\to \mathbb{R}^2$
45581
Is the distance function in a metric space (uniformly) continuous?
106256
Continuous mapping on a compact metric space is uniformly continuous