How to prove that UFD implies normal?
85782
UFDs are integrally closed
14759
Prove that $ f(z) = 0 $ for all $ z \in \overline{D}(0,1) $.
60723
Prove that if $A$ is normal, then eigenvectors corresponding to distinct eigenvalues are necessarily orthogonal (alternative proof)
24413
Why is $\mathbb{Z}[\sqrt{-n}], n\ge 3$ not a UFD?
105700
Proving $\,f$ is constant.
73454
Prove that $f$ has finite number of roots
152109
In a UFD if $x$ is irreducible, then $(x)$ is prime
12293
Let X be a T1 space, and show that X is normal if and only if each neighbourhood of a closed set F contains the closure of some neighbourhood of F
118049
Show that $\mathbb{R}^{\mathbb{R}} = U_{e} \oplus U_{o}$
57101
About the localization of a UFD
76292
Showing that $f$ is identically $0$ on $\mathbb{D}$
157925
How to prove that the implicit function theorem implies the inverse function theorem?
74501
$\delta : C([0,1])\to\mathbb{R}$, $f\mapsto f(0)$, with sup-norm is bounded but unbounded with one-norm.
71479
Is there some elementary proof of invariance of domain?
151958
How to show $f'(0)$ exist and is equal to $1$?
104949
How would I prove that this function is affine if $f(x+h)-f(x)=hf'(x)$?
104263
How to show that $f'(x)<2f(x)$