Abstract
As was seen in Chapter 12 of BFE, several Boolean-based algebraic structures have been studied, that is, algebras having as support a Boolean algebra and whose operations are Boolean functions; homomorphisms connecting such algebras and expressed by Boolean functions have also been investigated. Chapter 13 of BFE deals with Boolean arithmetic and Boolean geometry. The former means the study of divisibility between Boolean functions. In Boolean geometry the rôle of the space is played by a Boolean algebra and one looks for analogues of the basic concepts of geometry; for instance, a “good” analogue of the distance function is the symmeric difference d(x, y) = x + y. As was seen in BFE, Chapter 14, Boolean analysis replaces the real line by a Boolean algebra, while the functions dealt with are Boolean functions.
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© 2001 Springer-Verlag London
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Rudeanu, S. (2001). Boolean-based mathematics. In: Lattice Functions and Equations. Discrete Mathematics and Theoretical Computer Science. Springer, London. https://doi.org/10.1007/978-1-4471-0241-0_12
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DOI: https://doi.org/10.1007/978-1-4471-0241-0_12
Publisher Name: Springer, London
Print ISBN: 978-1-85233-266-2
Online ISBN: 978-1-4471-0241-0
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