Abstract
A number system consists of a continuous value mapping whose domain is a symbolic space of infinite words and whose range is the extended real line. We say that the value mapping is a symbolic extension of \(\overline{\mathbb {R}}\). Symbolic spaces and symbolic extensions are treated in symbolic dynamics which is based on the theory of compact metric spaces (see e.g., Hocking and Young [1]).
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Hocking, J.G., Young, G.S.: Topology. Dover Publications, New York (1961)
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Kůrka, P. (2016). Symbolic Dynamics. In: Dynamics of Number Systems. Studies in Systems, Decision and Control, vol 59. Springer, Cham. https://doi.org/10.1007/978-3-319-33367-0_2
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DOI: https://doi.org/10.1007/978-3-319-33367-0_2
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