Prove that $\mathbb{R}^n$ cannot be a finite union of its hyperplanes .
51397
If a field $F$ is such that $\left|F\right|>n-1$ why is $V$ a vector space over $F$ not equal to the union of $n$ proper subspaces of $V$
153747
Sub-dimensional linear subspaces of $\mathbb{R}^{n}$ have measure zero.
135814
Prove certain subsets of $\mathbb R^n$ are subspaces
85586
Proving $\mathbb{Q}$ isn't homeomorphic to $\mathbb{Z}$
75970
$\mathbb Z[1/2]$ is not finitely generated?
47251
Non-compactness of $\mathbb{R}$ with the cocountable topology
39114
Prove that a set in $\mathbb R^3$ is not an algebraic set
110957
No non-trivial clopen sets in $\mathbb{R}$? How to give a direct proof?
69046
Proof of $\mathbb{Q}$ is not cyclic
132386
Show that $(\mathbb{Q}^*,\cdot)$ and $(\mathbb{R}^*,\cdot)$ aren't cyclic
8291
If $n$ vectors are linearly independent, is their span $\mathbb{R}^n$?
107389
Show that the vector space of real functions is not finitely spanned
101095
Constructing an example s.t. $\operatorname{Hom}_R(M,N)$ is not finitely generated
15909
Bijection from $\mathbb R$ to $\mathbb {R^N}$
36044
Show $\Bbb R ^n$ with a finite set removed is still connected.
35569
Prove that $[0,1]$ isn't homeomorphic to $\mathbb{R}$
127575
Prove that Open Sets in $\mathbb{R}$ are The Disjoint Union of Open Intervals Without the Axioms of Choice