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Complementing Euclidean geometry by the notion of a point that is able to disappear and appear again makes it possible to describe the space of matter in the state of fractional dimension in the classical context and, thus, opens up new prospects in the development of chemistry as a scientific field inseparable from the principle of atomism. In particular, taking into account the nonarithmetic character of any transformation, it becomes possible to distinctly define the interests of chemistry in the era of nanotechnologies owing to the physically clear interpretation of various notions such as matter, a body, and the boundary between the body and matter that is at the stage of becoming. The subject of these interests can be actions that can affect not only the divisibility of initial reactants and reaction products but also the number system of a chemical process in combination with selection rules on the way from states of fractional dimension to states of integer dimension.

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