Why is $\mathbb{C}$ algebraically closed, but $\mathbb{R}$ isn't
60614
Why is it that Complex Numbers are algebraically closed?
21599
$(0,1)$ is an open subset of $\mathbb{R}$ but not of $\mathbb{R}^2$, when we think of $\mathbb{R}$ as the x-axis in $\mathbb{R}^2$. Prove this.
57967
Difference between $\mathbb C$ and $\mathbb R^2$
52629
Example 1, Sec. 22 in Munkres' TOPOLOGY, 2nd edition: How to verify that this map is closed?
56171
Is $K(X)$ never algebraically closed?
80202
Why is $[0, 1] \cap \mathbb{Q}$ not compact in $\mathbb{Q}$?
149095
$f(\mathbb{R}\setminus \mathbb{Q}) \subseteq \mathbb{Q}$ and $f(\mathbb{Q}) \subseteq \mathbb{R}\setminus \mathbb{Q}$ imply that $f$ is not continuous
66272
Is there a common notion of $\mathbb{R}^n$, for non-integer $n$?
34740
Do finite algebraically closed fields exist?
80735
Show that $C_0([a, b], \mathbb{R})$ is not $\sigma$-compact
84148
Why is $\mathbb{R}^2$ not a subspace of $\mathbb{R}^3$?
3296
Proof That $\mathbb{R} \setminus \mathbb{Q}$ Is Not an $F_{\sigma}$ Set
93111
Finiteness of the Algebraic Closure
149971
Closed unit disk homeomorphic to $\mathbb{R}^2$?
85032
$Q(\mathbb{Z}[t]) / \mathbb{Z}[t]$ is not injective
37904
Prove that the multiplicative groups $\mathbb{R} - \{0\}$ and $\mathbb{C} - \{0\}$ are not isomorphic.
134442
Can a matrix in $\mathbb{R}$ have a minimal polynomial that has coefficients in $\mathbb{C}$?