Why is the statement "all vector space have a basis" is equivalent to the axiom of choice?
110654
Vector Spaces and AC
141858
$\forall \vec{b} \in \mathbb{R}^n, B \vec{x} = \vec{b}$ is consistent is equivalent to....
37119
Determine Which of the following Sets is a Vector Space
98759
Proof of "Dual normed vector space is complete"
130865
Why is the axiom of choice separated from the other axioms?
51313
Extension of linearly independent set to a basis in an infinite dimensional vector space
87692
Basis and dimension of vector space
31509
Is axiom of choice necessary for proving that every infinite set has a countably infinite subset?
18913
How to find a basis for the intersection of two vector spaces in $\mathbb{R}^n$?
69766
Is every normed vector space, an inner product space
52596
A basis for $k(X)$ regarded as a vector space over $k$
137873
Problems that involves two facts in the definition of vector spaces
74465
One-dimensional vector space and it's subspaces
120311
Equivalence of Axiom of Regularity
146339
Proof of -(-v)=v in a vector space
155207
Confusion regarding one formulation of the Axiom of Choice.
33563
Is the axiom of choice used in the proof that every open set is the union of basis elements (Mukres, Lemma 13.1)