A Continuous Linear Bijection from $\ell^2$ Onto a Dense Subset of $\ell^2$ Whose Inverse is Everywhere Unboundedly Discontinuous

Abstract

In a prior paper [1] we showed that there is a nonlinear, continuous, dense bijection from $\ell^{2}$ onto a subset of $\ell^{2}$ whose inverse is everywhere unboundedly discontinuous. We now show that there is a linear, continuous, dense bijection whose inverse is everywhere unboundedly discontinuous.