The target programme of the author’s approach presented in the article includes the study of the methodological functions of concepts-toposes capable of uncovering the essence of changes in the life space of a society, changes caused by the increasing influence of the Internet. The main stages of the informatization of the modern society are presented in the article by toposes of late industrialism and information toposes of post-industrialism which have emerged in the “post” era. The toposes of late industrialism, which were formed at the early stages of the computer revolution, are characterized by a risk orientation and incompleteness in the technogenic and socio-cultural segments of industrialized countries. Information toposes, expressing the digital level of informatization in society, create a very extensive institutional system of a new type, where information markets become factors of the globalization of the information economy. At the same time, as noted in the article, conflicts and risks of an economic, institutional and political nature appear in the information toposes. It seems expedient to develop the categorical apparatus of the topological approach further in the research of information processes in the living space of Russian society.