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A second countable space is a topological space whose topology is second countable.

Given an ideal A, a semiprime ring is one for which A^n=0 implies A=0 for any positive n. Every prime ring is semiprime.

The dual polyhedron of the small dodecicosidodecahedron U_(33) and Wenninger dual W_(72).

An affine transformation that preserves area.

A three-dimensional knot spun about a plane in four dimensions. Unlike suspended knots, spun knots are smoothly embedded at the poles.

A knot used to prevent the end of a string from slipping through a hole.

The structure constant is defined as iepsilon_(ijk), where epsilon_(ijk) is the permutation symbol. The structure constant forms the starting point for the development of Lie ...

For a subgroup H of a group G, the index of H, denoted (G:H), is the cardinal number of the set of left cosets of H in G (which is equal to the cardinal number of the set of ...

A submersion is a smooth map f:M->N when dimM>=dimN, given that the differential, or Jacobian, is surjective at every x in M. The basic example of a submersion is the ...

Given any two distinct points x,y, there exist neighborhoods u and v of x and y, respectively, with u intersection v=emptyset. It then follows that finite subsets are closed.