Let $X$ be complete and $f:X \to Y$ bilipschitz. Show that $f(X)$ is complete.
35804
Bi-Lipschitz map preserves completeness
80397
Show that this set of polynomials is ideal in F[x]
103340
Show that this entire function is polynomial.
102553
How to show that $f(z) = f(i)$
41482
$f_n → f$ uniformly on $S$ and each $f_n$ is cont on $S$. Let $(x_n)$ be a sequence of points in $S$ converging to $x \in S$. Then $f_n(x_n) → f(x)$.
51227
Proving that given metric space is complete: $X := (0,\infty)$ and $d:=|\ln(x)-\ln(y)|$
13174
Show that $A[X]/(aX+b)$ is an integral domain
126461
Show that $g:I\to\mathbb{R}$ is continuous and $f:(x-x_0)g(x)$ is differentiable
36099
Show that $\|f\|^{2}$ attains a minimum value on the interior of $B$
15727
show that if $f$ is uniformly differentiable then prove that $f'$ is continuous
128894
About compactness and completeness of set $X = \mathbb{R}$ with the metric $d(x, y) = \frac{|x-y|}{1+|x-y|}$
7358
For each $y \in \mathbb{R}$ either no $x$ with $f(x) = y$ or two such values of $x$. Show that $f$ is discontinuous.
72044
prove $x \mapsto x^2$ is continuous
129856
Show that $f(x)=\frac{x}{1+|x|}$ is uniformly continuous.
155923
continuity of $f(x,y)$ in $\mathbb R^2$.
45642
Prove that the Extension Theorem is Complete.
28399
Showing $f$ is constant