The classical density topology is the topology generated by the lower density operator connected with a density point of a set. One of the possible generalizations of the concept of a density point is replacing the Lebesgue measure by the outer Lebesgue measure. It turns out that the analogous family associated with such generalized density points is not a topology. In this case, one can prove that this family is a strong generalized topology. In the paper some properties of the strong generalized topology connected with density points with respect to the outer Lebesgue measure will be presented. Moreover, among others, some characterizations of the families of meager sets and compact sets in this space will be given.

经典密度拓扑是由较低密度算子与集合的密度点连接而生成的拓扑。密度点概念的一种可能的概括是用外部Lebesgue测度代替Lebesgue测度。事实证明，与这种广义密度点关联的类似族不是拓扑。在这种情况下，可以证明该族是一个强大的广义拓扑。在本文中，将介绍与外部Lebesgue测度有关的，与密度点相关的强广义拓扑的一些属性。此外，除其他外，还将给出该空间中的微分集和紧集的族的一些特征。