一句话：提出重叠代数可构造地刻画几乎离散 locale，并在 LEM 下与 Boolean locale 一致。
经典地，Boolean locale 是“几乎离散”的：空间化后恰为离散 locale。但该事实依赖排中律，不能构造性证明；构造性地看，除平凡情形外离散 locale 从不是 Boolean。本文追问构造性意义下何为几乎离散 locale，并主张 Sambin 的重叠代数是合适候选。作者证明重叠代数包含离散 locale，可作为 overt locale 的最小强稠密 sublocale 得到，并在 LEM 成立时恰好与 Boolean locale 重合。
Boolean locales are "almost discrete", in the sense that a spatial Boolean locale is just a discrete locale (that is, it corresponds to the frame of open subsets of a discrete space, namely the powerset of a set). This basic fact, however, cannot be proven constructively, that is, over intuitionistic logic, as it requires the full law of excluded middle (LEM). In fact, discrete locales are never Boolean constructively, except for the trivial locale. So, what is an almost discrete locale constructively? Our claim is that Sambin's overlap algebras have good enough features to deserve to be called that. Namely, they include the class of discrete locales, they arise as smallest strongly dense sublocales (of overt locales), and hence they coincide with the Boolean locales if LEM holds.