A union of two subspaces not equal to the vector space.
11301
Union of two vector subspaces not a subspace?
106670
Existence of vector space complement and axiom of choice
53633
Given two subspaces $U,W$ of vector space $V$, how to show that $\dim(U)+\dim(W)=\dim(U+W)+\dim(U\cap W)$
18913
How to find a basis for the intersection of two vector spaces in $\mathbb{R}^n$?
90826
Constructing a subset not in $\mathcal{B}(\mathbb{R})$ explicitly
117185
The union of a strictly increasing sequence of $\sigma$-algebras is not a $\sigma$-algebra
107000
Dimension of intersection of distinct subspaces
27899
Can we prove the existence of $A\cup B$ without the union axiom?
78833
Can a basis for a vector space $V$ can be restricted to a basis for any subspace $W$?
85819
A non-polyhedral pair $(X,A)$ with both $X$ and $A$ polyhedral
139988
Counter example for a result of intersection of subspaces
18423
Subspace of Lindelöf space is not Lindelöf: Example
41347
The dimension of the intersection of two vector subspaces
15560
Prove that the union of three subspaces of $V$ is a subspace iff one of the subspaces contains the other two.
45111
Number of Subspaces that contains other Space
150135
The intersection of an infinite number of subspaces is a subspace
64840
A Banach space that is not a Hilbert space