Prove that $\mathbb R^n$ is not the union of finitely many its proper subspaces.
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 $V$
7607
How to prove that $\mathbb{Q}$ is not the intersection of a countable collection of open sets.
48783
Prove that the sum of two compact sets in $\mathbb R^n$ is compact.
723
Is there a constructive way to exhibit a basis for $\mathbb{R}^\mathbb{N}$?
128732
$\mathbb Z_{p^n}$ is not the direct product of any family of its proper subgroups
95635
$\ell^{\infty}(\mathbb N)$ is not a separable space
80735
Show that $C_0([a, b], \mathbb{R})$ is not $\sigma$-compact
84148
Why is $\mathbb{R}^2$ not a subspace of $\mathbb{R}^3$?
92740
prove that $\mathbb{Q}^n$is dense subset of $\mathbb{R^n}$
67259
Can we prove that a bounded closed subset of $\mathbb R^n$ is compact without Axiom of Choice?
43504
Proving the existence of a complement subspace $U' \subset V$.
99300
Prove if $W \subset V$ is a subspace such that $T(W)\subset W$, then $V/W$ is finite-dimensional.
14713
$X=(-\infty,0]\cup\left\{{1\over n}:n\in\mathbb N\right\}$ with subspace topology Then
148507
Why an open set in $R^n$ might not be written as countable union of disjoint open intervals?
41872
Show that $\mathbb{R}^2$ is not homeomorphic to $\mathbb{R}^2 \setminus\{(0,0)\}$
69206
A finite-dimensional vector space cannot be covered by finitely many proper subspaces?
134065
A question about an $n$-dimensional subspace of $\mathbb{F}^{S}$.