Let (X,d) a metric space. Show that a function is continuous
45581
Is the distance function in a metric space (uniformly) continuous?
7402
Showing a compact metric space has a countable dense subset
129856
Show that $f(x)=\frac{x}{1+|x|}$ is uniformly continuous.
82333
let $(X,d)$ be a metric space. How I can show that any finite subset of $X$ is closed.
154559
For each $x\in X$ there exists a neighborhood of x s.t $A\cap U\neq \emptyset$ for only finitely many $A\in\mathcal{A}$. Show that f is continuous.
100740
proof of that a continuous function has a fixed point
111907
Prove that Cantor function is Hölder continuous
100187
Show function is continuous at origin
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 $a$
46834
show that a distance function is continuous
77621
Continuity of function mapping connected set to connected set
75479
Proving that this function is continuous on $G\times G$
72044
prove $x \mapsto x^2$ is continuous
17234
Show that a continuous function has a fixed point
152493
Is an expanding map on a compact metric space continuous?
131992
A problem on continuous functions
130537
Proving that $d(f,g)=\|f-g\| = \sup \limits_{0\leq x \leq 1} |f(x)-g(x)|$ is a metric on $X=C[0,1]$