The paper discusses M.A. Balaban's paradigm within which knowledge is viewed not as a tool acquired by the individual, but as an organ for segmenting the perceptual field developing under the influence of the environment. On the basis of this paradigm the author suggests an approach to modeling knowledge and the cognitive process. General topology is the main modeling tool. Knowledge is viewed as topology on the individual's perceptual field, the cognitive process - as a chain of topologies superimposed over one another. The paper explains the notions of image, association, concept, communication. The author also suggests an approach to describing the mechanisms of insight by means of general topology.