Weakly Boolean maximal chains of homeomorphic topologies

Abstract

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