$K(X)$ is not algebraically closed
56171
Is $K(X)$ never algebraically closed?
97004
Algebraic closure not even finitely generated over base field
42652
Must $k$-subalgebra of $k[x]$ be finitely generated?
3896
A closed set in $(A, \mathcal T_A)$ that is not closed in $(X, \mathcal T)$
7607
How to prove that $\mathbb{Q}$ is not the intersection of a countable collection of open sets.
46698
Showing a set is closed under inverses
82824
Affine algebraic subset of $\mathbb{A}_k^4$
148994
$K \subset \mathbb{R}^n$ is compact iff it is closed and bounded
136538
How can I show that a bijection between $[0,1)$ and $(0,1)$ cannot be continuous?
98391
example of a nonempty subset is closed under scalar multiplication but not a subspace
158590
Why is it that if $[L:K]$ is finite, then $[L:K]$ is algebraic?
11698
$M /K \land L /K$ algebraic $\implies ML/K$ algebraic?
4192
Non-algebraically closed field in which every polynomial of degree $<n$ has a root
108156
Algebraic closure of $\mathbb{C}(x)$ is isomorphic to $\mathbb{C}$
153100
A counterexample to "$k\mid n$ if and only if $k\mid n^2$"
111338
Affine variety over a field which is not algebraically closed can be written as the zero set of a single polynomial
108408
Example of quotient mapping that is not open