Weakly Boolean maximal chains of homeomorphic topologies

If $\lambda <\kappa$ are infinite cardinals, a linear order $L$ is isomorphic to a maximal chain in $[\kappa {]}^{\kappa \mathrm{\mid }\kappa }$ (resp. $[\kappa {]}^{\lambda \mathrm{\mid }\kappa }$; $[\kappa {]}^{\kappa \mathrm{\mid }\lambda }$) iff $L$ is weakly Boolean, the weight of all initial segments of $L$ is equal to $\kappa$ (resp. $\lambda$, ${\lambda }^{+}$) and the weight of all final segments of $L$ is equal to $\kappa$ (resp. ${\lambda }^{+}$, $\lambda$). We also provide an application of this result in topology.