2 problems

Let $\mathcal{X}$ be a separable Banach space. A dense subspace $\mathcal{Y}$ of $\mathcal{X}$ has dimension continuum when its linear dimension is the cardinality of the continuum…

Let $\Psi$ be the linearly ordered set constructed above, and let $\mathscr{C}_0(\Psi)$ denote the space of continuous functions on $\Psi$ vanishing at the relevant endpoint. A Gât…