Show that if a normed space $X $ has a linearly independent subset of $n$ elements, so does the dual space $X'$
100161
Is it true that $\dim(X) \leq \dim(X^{\ast})$ for every infinite dimentional Banach space $X$?
135694
Proving $\kappa^{\lambda} = |\{X: X \subseteq \kappa, |X|=\lambda\}|$
51313
Extension of linearly independent set to a basis in an infinite dimensional vector space
92534
Prove that any finite subset of a linearly independent set is linearly independent
14215
Show that the union $\bigcup A_n$ has empty interior in $X$
58447
Is axiom of choice required for there to be an infinite linearly independent set in a (non-finite-dimensional) vector space?
139272
On the norm of a quotient of a Banach space.
41611
Open and closed set in n by n matrices space.
14713
$X=(-\infty,0]\cup\left\{{1\over n}:n\in\mathbb N\right\}$ with subspace topology Then
66500
Proving that orthogonal vectors are linearly independent
151161
norms on vector space are equivalent iff they have same topology
83665
Prove a assertion concerning Lebesgue space
8291
If $n$ vectors are linearly independent, is their span $\mathbb{R}^n$?
126744
Is any Banach space a dual space?
102529
Prove that the set $\left\{ x, Ax, \dots, A^{k-1} x \right\}$ is linearly independent
82334
For $f$ in dual space, there exists $x$ with norm 1 and $f(x)=\|f\|$ if space is reflexive (and nontrivial)
91173
Finite-dimensional subspace normed vector space is closed