Pseudogroup

In mathematics, a pseudogroup is an extension of the group concept, but one that grew out of the geometric approach of Sophus Lie, rather than out of abstract algebra (such as quasigroup, for example). A theory of pseudogroups was developed by Élie Cartan in the early 1900s. In mathematics, a pseudogroup is an extension of the group concept, but one that grew out of the geometric approach of Sophus Lie, rather than out of abstract algebra (such as quasigroup, for example). A theory of pseudogroups was developed by Élie Cartan in the early 1900s. It is not an axiomatic algebraic idea; rather it defines a set of closure conditions on sets of homeomorphisms defined on open sets U of a given Euclidean space E or more generally of a fixed topological space S. The groupoid condition on those is fulfilled, in that homeomorphisms