In the conventional science such as physics, the world is recognized as a priori existence. However, its recognition lacks such a viewpoint that the world emerges through our consciousness. In this study, from this viewpoint, the emerging world is described by mathematics; the mathematics is a language or tool which describes phenomena in the modern science. Concretely, general topology is used in the field of mathematics; the general topology describes abstract notions, especially, the morphology of notions. Then, by the use of the author’s original notion, primitive chaos, such a situation that the world is emerging is pictured along with the notions of events, causality, a nested structure, decomposition, hierarchy, self-similarity, part and whole, continuance and discreteness, coarse graining, identifying, embedding, logic, and so on

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