"Every vector space over $\mathbb{Q}$ has a basis" $\Leftrightarrow$ Axiom of choice?
43503
Bases of complex vector spaces and the axiom of choice
83116
Uncountability of basis of $\mathbb R^{\mathbb N}$
68526
Polynomials as vector spaces?
141714
Existence of a functor $\mathsf{Sets} \to \mathsf{Groups}$ that admits a left adjoint
78833
Can a basis for a vector space $V$ can be restricted to a basis for any subspace $W$?
26497
Take $\mathbb{R}$ as a vector space over $\mathbb{Q}$, then a basis for $\mathbb{R}$, then $|B|=2^{\aleph_0}$
76498
Does every linearly independent set of n vectors in $R^n$ forms a basis in $R^n$?
92510
Proving a vector space is infinite-dimensional
94929
Proof that the all bases of a subspace V consist of the same number of vectors?
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 $V$
87451
Construction of matrices under ZFC axioms
110654
Vector Spaces and AC
155125
Every ordered field has a subfield isomorphic to $\mathbb Q$?
106101
Why there is much interest in the study of $\operatorname{Gal}\left(\overline{\mathbb Q}/\mathbb Q\right)$?
52596
A basis for $k(X)$ regarded as a vector space over $k$
152742
Finding a basis of an infinite-dimensional vector space?
723
Is there a constructive way to exhibit a basis for $\mathbb{R}^\mathbb{N}$?