# Tagged Questions

**3**

votes

**1**answer

142 views

### Algebras with countable chains only

Is there an example of an uncountable Boolean algebra $B$ in which every chain is countable and such that $\ell_\infty$ embeds into the Banach space $C(\mbox{Stone }B)$? The latter requirement is not ...

**4**

votes

**1**answer

216 views

### Density character of $\ell_\infty(\kappa, S)$

Let $S$ be an uncountable set. Consider the subspace $\ell_\infty(\kappa, S)$ of $\ell_\infty(S)$ formed by all functions with support of cardinality at most $\kappa$ (here $\kappa<|S|$). ...

**2**

votes

**1**answer

253 views

### Uniqueness of dimension in Banach spaces

Let $\;\;\; \big\langle V,+,\cdot, \;\; ||\cdot|| \;\; \big\rangle \;\;\;$ be a Banach space over the field $\mathbb{K}$, which is either $\mathbb{R}$ or $\mathbb{C}$.
Suppose there exists a subset ...

**3**

votes

**3**answers

381 views

### Shape of long sequences in C(ω_1)

Apologies for the vague title - I couldn't come up with a single sentence that summarised this problem well. If you can, please edit or suggest a better one!
This question is also rather specific and ...