Is it required to use choice principles to prove that any linearly independent set can be extended to a basis?
58447
Is axiom of choice required for there to be an infinite linearly independent set in a (non-finite-dimensional) vector space?
65308
Axiom of Choice: Family of non-empty sets mutually disjoint or not?
69337
Zorn's Lemma And Axiom of Choice
61747
Proof of exchange principle in set theory
150385
The use of the Axiom of Choice in this proof of the sequence lemma
95928
Independence and orthogonality
144557
Linearly independent functionals
120064
Proving that without the axiom of choice there is a set with an accumulation point that isn'tthe limit of a convergeant sequence
62058
How to prove $1$,$\sqrt{2},\sqrt{3}$ and $\sqrt{6}$ are linearly independent over $\mathbb{Q}$?
40409
If a subspace S is spanned by $n$ vectors, any subset of S with $m>n$ vectors is linearly dependent
50506
What concept does an open set axiomatise?
105791
Does separability imply the Lindelöf property?
102202
The smallest infinity and the axiom of choice
96354
Linear independence of $\sin(x)$, $\sin(2x)$, $\sin(3x)$ in Map($\mathbb{R},\mathbb{R}$)
12539
Set Theory: Equivalency of Axiom of Choice and Choice Function
30968
Is it possible that every set can be specified?
147908
Why use the biconditional in the Axiom of Extensionality