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Many authors (e.g., Mendelson 1963; Pervin 1964) use the term arcwise-connected as a synonym for pathwise-connected. Other authors (e.g., Armstrong 1983; Cullen 1968; and ...

The quantum electrodynamical law which applies to spin-1/2 particles and is the relativistic generalization of the Schrödinger equation. In 3+1 dimensions (three space ...

The direct product is defined for a number of classes of algebraic objects, including sets, groups, rings, and modules. In each case, the direct product of an algebraic ...

"Escher's solid" is the solid illustrated on the right pedestal in M. C. Escher's Waterfall woodcut (Bool et al. 1982, p. 323). It is obtained by augmenting a rhombic ...

Gauge theory studies principal bundle connections, called gauge fields, on a principal bundle. These connections correspond to fields, in physics, such as an electromagnetic ...

In general, it is possible to link two n-dimensional hyperspheres in (n+2)-dimensional space in an infinite number of inequivalent ways. In dimensions greater than n+2 in the ...

A natural equation is an equation which specifies a curve independent of any choice of coordinates or parameterization. The study of natural equations began with the ...

Let L be a finite-dimensional split semisimple Lie algebra over a field of field characteristic 0, H a splitting Cartan subalgebra, and Lambda a weight of H in a ...

The Spencer-Brown form is a simple mathematical concept that formalizes what a mathematical object is formally identical to what it is not (Spencer-Brown 1997, pp. ix and ...

Vassiliev invariants, discovered around 1989, provided a radically new way of looking at knots. The notion of finite type (a.k.a. Vassiliev) knot invariants was independently ...