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Autometrized Boolean Algebras I:Fundamental Distance-Theoretic Properties of B

Published online by Cambridge University Press:  20 November 2018

David Ellis
David Ellis*
Affiliation:
University of Missouri
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There have been several brief studies made [3, 4, 7, 8, 9, 11] of systems in which a “distance function” is defined on the set of pairs of elements of some abstract set to another abstract set. Frequently both of the sets involved are given algebraic structures. One of the more novel of these systems is the naturally metrized group [3, 7] originated by Karl Menger in 1931. This system is analogous to the Euclidean line in that it assigns to each pair, a, b of elements of an additively written Abelian group the “absolute value”, (a-b, b-a) = (b-a, a-b), of the "difference" of the elements as ”distance“.

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 3 , 1951 , pp. 87 - 93
Copyright
Copyright © Canadian Mathematical Society 1951

References

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