Does existence of nonzero linear functional depends on axiom of choice?
112548
Existence of non-trivial linear functional on any vector space
120311
Equivalence of Axiom of Regularity
108329
If $T\alpha=c\alpha$, then there is a non-zero linear functional $f$ on $V$ such that $T^{t}f=cf$
109926
Axiom of Regularity and infinite sequences
72006
Suppose $f(x)$ is linear i.e. $f(x + y) = f(x) +f(y) $ and monotone on $[-\infty, +\infty]$, then $f(x) = ax$, a real.
58631
Continuity and the Axiom of Choice
50451
The linear dependence of exponential functions
146188
Why does a proof of $\exists f: X\to Y$ injection $\iff \exists g: Y \to X$ surjection requires the axiom of choice?
121732
Functional completeness of $\{\text{or},\text{ xor}, \text{ xnor}\}$
90435
Prove that there exist linear functionals $L_1, L_2$ on $X$
58816
Existence of a continuous function which does not achieve a maximum.
154521
Linear functional $f$ is continuous at $x_0=0$ if and only if $f$ is continuous $\forall x\in X$?
139992
Is power-associativity finitely axiomatizable?
87655
Consequence of the Hahn-Banach Theorem
105815
Does proving (second countable) $\Rightarrow$ (Lindelöf) require the axiom of choice?
7214
Does linear ordering need the Axiom of Choice?
119947
Can a non-zero vector have zero image under every linear functional?