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Pseudomathematics, or mathematical crankery, is a mathematics-like activity that does not adhere to the framework of rigor of formal mathematical practice. Common areas of pseudomathematics are solutions of problems proved to be unsolvable or recognized as extremely hard by experts, as well as attempts to apply mathematics to non-quantifiable ...
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In mathematics, a pseudogroup is a set of homeomorphisms between open sets of a space, satisfying group-like and sheaf-like properties. It is a generalisation [dubious – discuss] of the concept of a group, originating however from the geometric approach of Sophus Lie [1] to investigate symmetries of differential equations, rather than out of abstract algebra (such as quasigroup, for example).
The metric of a pseudo-Riemannian manifold, a non-degenerate, smooth, symmetric tensor field of arbitrary signature Pseudometric space , a generalization of a metric that does not necessarily distinguish points (and so typically used to study certain non-Hausdorff spaces)
The vanishing of the pseudometric induces an equivalence relation, called the metric identification, that converts the pseudometric space into a full-fledged metric space. This is done by defining x ∼ y {\displaystyle x\sim y} if d ( x , y ) = 0 {\displaystyle d(x,y)=0} .
In mathematical physics, a pseudo-Riemannian manifold, [1] [2] also called a semi-Riemannian manifold, is a differentiable manifold with a metric tensor that is everywhere nondegenerate. This is a generalization of a Riemannian manifold in which the requirement of positive-definiteness is relaxed.