A Ternary Algebraic Operation in the Theory of Coordinate Structures

Christopher D. Hollings and Mark V. Lawson
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Christopher D. Hollings: University of Oxford, Mathematical Institute
Mark V. Lawson: Heriot-Watt University, Department of Mathematics

Chapter Chapter 5 in Wagner’s Theory of Generalised Heaps, 2017, pp 31-35 from Springer

Abstract: Abstract In this short communication to the Academy of Sciences, Wagner took 𝔐 ( A × B ) $$\mathfrak{M}(A \times B)$$ to be the collection of all one-to-one partial mappings from a set A to a set B. A coordinate structure K on A is a subset of 𝔐 ( A × B ) $$\mathfrak{M}(A \times B)$$ . A ternary operation can be defined in 𝔐 ( A × B ) $$\mathfrak{M}(A \times B)$$ by (φ 3 φ 2 φ 1) = φ 3 φ 2 −1 φ 1, where−1 indicates the inverse of an injective partial mapping. Wagner’s main interest was in those coordinate structures that have closure properties with respect to this operation. The purpose of this paper seems to have been to introduce this formulation as a means of providing an abstract description of coordinate structures in differential geometry.

Keywords: Coordination Structure; Partial Injective Function; Ternary Operation; Triple Multiplication; Empty Binary Relation (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-63621-4_5

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DOI: 10.1007/978-3-319-63621-4_5

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