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A Turing machine which, by appropriate programming using a finite length of input tape, can act as any Turing machine whatsoever. In his seminal paper, Turing himself gave ...

Just as the ratio of the arc length of a semicircle to its radius is always pi, the ratio P of the arc length of the parabolic segment formed by the latus rectum of any ...

Let h:{0,1}^(l(n))×{0,1}^n->{0,1}^(m(n)) be efficiently computable by an algorithm (solving a P-problem). For fixed y in {0,1}^(l(n)), view h(x,y) as a function h_y(x) of x ...

Deck transformations, also called covering transformations, are defined for any cover p:A->X. They act on A by homeomorphisms which preserve the projection p. Deck ...

A refinement X of a cover Y is a cover such that every element x in X is a subset of an element y in Y.

Given a smooth manifold M with an open cover U_i, a partition of unity subject to the cover U_i is a collection of smooth, nonnegative functions psi_i, such that the support ...

The Lebesgue covering dimension is an important dimension and one of the first dimensions investigated. It is defined in terms of covering sets, and is therefore also called ...

A subset S of a topological space X is compact if for every open cover of S there exists a finite subcover of S.

The bipartite double graph, also called the Kronecker cover, Kronecker double cover, bipartite double cover, canonical double cover, or bipartite double, of a given graph G ...

A curve on the surface of a sphere. Examples include the baseball cover, Seiffert's spherical spiral, spherical helix, and spherical spiral.