Proving that the union of two vector sub spaces of the same space are not a sub space.
11301
Union of two vector subspaces not a subspace?
80735
Show that $C_0([a, b], \mathbb{R})$ is not $\sigma$-compact
39114
Prove that a set in $\mathbb R^3$ is not an algebraic set
12189
Prove norm doesn't come from inner product.
27899
Can we prove the existence of $A\cup B$ without the union axiom?
139841
Proving $A\setminus(B\setminus C)$ is not equal to $(A\setminus B)\setminus C$
34272
Proving definition of norms induced by vector norms
3296
Proof That $\mathbb{R} \setminus \mathbb{Q}$ Is Not an $F_{\sigma}$ Set
99300
Prove if $W \subset V$ is a subspace such that $T(W)\subset W$, then $V/W$ is finite-dimensional.
70413
A vector space over $R$ is not a countable union of proper subspaces
121810
Prove that the product of two infinite cyclic groups is not infinite cyclic.
49385
Proving $\forall x (A\to B) \to(A \to \forall x B):x\notin \mbox{free}(A)$ in a Hilbert system where it is not an axiom
22295
Subspace of a separable space is separable
153747
Sub-dimensional linear subspaces of $\mathbb{R}^{n}$ have measure zero.
95513
Proving $W$ is a subspace of $P_{2}$
63285
Prove that this space is not Banach
54737
Proof that $V = \sum_k U_k$ and $\dim V=\sum_k \dim U_k$ implies $V=\oplus_k U_k$