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A Ternary Algebraic Operation in the Theory of Coordinate Structures

In: Wagner’s Theory of Generalised Heaps

Author

Listed:
  • Christopher D. Hollings

    (University of Oxford, Mathematical Institute
    The Queen’s College)

  • Mark V. Lawson

    (Heriot-Watt University, Department of Mathematics)

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.

Suggested Citation

  • Christopher D. Hollings & Mark V. Lawson, 2017. "A Ternary Algebraic Operation in the Theory of Coordinate Structures," Springer Books, in: Wagner’s Theory of Generalised Heaps, chapter 0, pages 31-35, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-63621-4_5
    DOI: 10.1007/978-3-319-63621-4_5
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