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 (φ3φ2φ1) = φ3φ2−1φ1, 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.
Published Version
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