$\mathbb{R}^{n}$ is not the union of only finitely many (proper) affine subsets.
69206
A finite-dimensional vector space cannot be covered by finitely many proper subspaces?
15491
Prove that $f:\mathbb R^n\to\mathbb R$ is affine if and only if it is convex and concave
125043
Show that F(A−B) is not necessarily a subset of F(A)−F(B).
67279
Is the union of finitely many open sets in an omega-cover contained within some member of the cover?
158569
Proving a particular subset of $R^n$ is closed
28819
A union of two subspaces not equal to the vector space.
80827
Let $A$ be a nonempty subset of $\mathbb{R}$. Prove...
134065
A question about an $n$-dimensional subspace of $\mathbb{F}^{S}$.
85099
How many subsets of $\mathbb{N}$ have the same cardinality as $\mathbb{N}$?
22464
Which of the following subsets of   $\mathbb{R}^2$ are compact
71173
Show that $\mathbb{A}^n$ on the Zariski Topology is not Hausdorff, but it is $T_1$
158498
$A\subset \mathbb{R}$ with more than one element and $A/ \{a\}$ is compact for a fixed $a\in A$
128732
$\mathbb Z_{p^n}$ is not the direct product of any family of its proper subgroups
41661
Show that the set of all finite subsets of $\mathbb{N}$ is countable.
126927
$\mathbb Q$ is not the direct product of two non-trivial groups.
65494
Proper subspaces of $ R^n $
88645
Prove that the additive groups $\mathbb{R}$ and $\mathbb{Q}$ are not isomorphic.