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The trivial loop is the loop that takes every point to its basepoint. Formally, if X is a topological space and x in X, the trivial loop based at x is the map L:[0,1]->X ...

A differential ideal I on a manifold M is an ideal in the exterior algebra of differential k-forms on M which is also closed under the exterior derivative d. That is, for any ...

A module homomorphism is a map f:M->N between modules over a ring R which preserves both the addition and the multiplication by scalars. In symbols this means that ...

A subset M subset R^n is called a regular surface if for each point p in M, there exists a neighborhood V of p in R^n and a map x:U->R^n of an open set U subset R^2 onto V ...

A Cantor set C in R^3 is said to be scrawny if for each neighborhood U of an arbitrary point p in C, there is a neighborhood V of p such that every map f:S^1->V subset C ...

Let f:M|->N be a map between two compact, connected, oriented n-dimensional manifolds without boundary. Then f induces a homomorphism f_* from the homology groups H_n(M) to ...

An Anosov diffeomorphism is a C^1 diffeomorphism phi of a manifold M to itself such that the tangent bundle of M is hyperbolic with respect to phi. Very few classes of Anosov ...

A map projection which is a conformal mapping, i.e., one for which local (infinitesimal) angles on a sphere are mapped to the same angles in the projection. On maps of an ...

A complex rotation is a map of the form z|->ze^(itheta), where theta is a real number, which corresponds to counterclockwise rotation by theta radians about the origin of ...

One of the seven 4-polyhexes. S. Kim has observed that four worms solve the puzzle of finding a non-three-colorable map with only four congruent countries (as long as no ...