# Tagged Questions

**7**

votes

**1**answer

380 views

### Non continuous Linear form on $E=C([0,1],\mathbb{R})$ without AC

Let's note $E=C([0,1],\mathbb{R})$ the Banach space of real continuous funtions from the [0,1] interval with the uniform norm.
Is it possible to show a non-continuous linear form on $E$ exists ...

**9**

votes

**1**answer

310 views

### Inequivalent complete norms and the axiom of choice

Hi,
I've been wondering about the following :
Is it possible, without the axiom of choice, to have two inequivalent complete norms on a vector space?
All the examples of inequivalent complete norms ...

**5**

votes

**0**answers

1k views

### Explicit element of $(\ell^{\infty})^* - \ell^1$? [duplicate]

Possible Duplicate:
What’s an example of a space that needs the Hahn-Banach Theorem?
It is well known that the dual of $\ell^{\infty}$ properly contains $\ell^1$ (over $\mathbb{N}$, ...