Show that the space D with the metric ρ is separable. Let Show that this is a Cauchy sequence with respect to ρ, but does not converge to an element of D. Show {fn} is not a Cauchy sequence with...

Show that the space D with the metric ρ is separable.

Let

Show that this is a Cauchy sequence with respect to ρ, but does not converge to an element of D. Show {fn} is not a Cauchy sequence with respect to d.

Show that (with respect to the topology on D) the subset C[0, 1] of D is nowhere dense.

Consider D with the metric

Show that D is not separable with respect to the metric d_sup.