Anzeige
Erschienen in:
2017 | OriginalPaper | Buchkapitel
5. A Ternary Algebraic Operation in the Theory of Coordinate Structures
verfasst von : Christopher D. Hollings, Mark V. Lawson
Erschienen in: Wagner’s Theory of Generalised Heaps
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
Abstract
In this short communication to the Academy of Sciences, Wagner took \(\mathfrak{M}(A \times B)\) 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 \(\mathfrak{M}(A \times B)\). A ternary operation can be defined in \(\mathfrak{M}(A \times B)\) 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.