Is $\mathbf{R}$ a subspace of a vector space over $\mathbf{Q}$ that has a basis without choice?
106625
Strength of the statement "$\mathbb R$ has a Hamel basis over $\mathbb Q$"
106670
Existence of vector space complement and axiom of choice
70413
A vector space over $R$ is not a countable union of proper subspaces
76498
Does every linearly independent set of n vectors in $R^n$ forms a basis in $R^n$?
1475
In an incomplete inner product space, is a closed linear subspace equal to the orthogonal complement of its orthogonal complement?
28402
Number of bases of an n-dimensional vector space over q-element field.
15020
How to count number of bases and subspaces of a given dimension in a vector space over a finite field?
112548
Existence of non-trivial linear functional on any vector space
139951
Direct Sum of vector subspaces
137769
How to find a basis for a subspace?
74465
One-dimensional vector space and it's subspaces
117131
Canonical Isomorphism Between $\mathbf{V}$ and $(\mathbf{V}^*)^*$
11301
Union of two vector subspaces not a subspace?
74623
Associative rule of subspaces and vector spaces: $(U+V) \cap W = U + (V \cap W)$
28819
A union of two subspaces not equal to the vector space.
17748
Is there a quick proof as to why the vector space of $\mathbb{R}$ over $\mathbb{Q}$ is infinite-dimensional?
154724
Every vector space has a basis