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An algebraic variety over a field K that becomes isomorphic to a projective space.

A subset of a topological space is called clopen if it is both closed and open.

A subset of a topological space which is compact with respect to the relative topology.

A subset A subset= X of a topological space X is said to be disconnected if it is not connected.

The kernel of a linear transformation T:V-->W between vector spaces is its null space.

A nonsimply connected 3-manifold, also called a dodecahedral space.

The hypothesis is that, for X is a measure space, f_n(x)->f(x) for each x in X, as n->infty. The hypothesis may be weakened to almost everywhere convergence.

A local-ringed space which is locally isomorphic to an affine scheme.

A subset M of a Hilbert space H is a linear manifold if it is closed under addition of vectors and scalar multiplication.

In the plane, there are 17 lattice groups, eight of which are pure translation. In R^3, there are 32 point groups and 230 space groups. In R^4, there are 4783 space lattice ...