Metric is continuous function
23845
How to prove the continuity of the metric function?
86327
If the absolute value of a function is continuous, is the function continuous?
16060
Showing this metric space is complete
126944
Metric spaces problem
118207
Prove that the product of two continuous functions is continuous
130023
Prove that the sum of two continuous functions is continuous
124688
Question about a metric on $\mathbb{R}^2$
45581
Is the distance function in a metric space (uniformly) continuous?
114047
Metric $d(x,y)=\frac{|x-y|}{\sqrt{1+x^2}\sqrt{1+y^2}}$ on $\mathbb{R}$
152493
Is an expanding map on a compact metric space continuous?
12349
a construction of a continuous function from a normal space to [0,1]
85242
Deciding whether two metrics are topologically equivalent in the space $C^1([0,1])$
65840
Norm induced by metric
57023
If $f,g$ are continuous at $a$, show that $h(x)=\max\{f(x),g(x)\}$ and $k(x)=\min\{f(x),g(x)\}$ are also continuous at $a$
64260
Prove that a function between metric spaces is continuous iff the inverse image of a closed set is closed
52014
Showing $(C[0,1], d_1)$ is not a complete metric space
153495
Continuous function does not map closed set to closed set