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A union-closed set is a nonempty finite collection of distinct nonempty finite sets which is closed under union.

A uniquely complemented lattice is a complemented lattice (L, ^ , v ,0,1,^') that satisfies ( forall x in L)( forall y in L)[(x ^ y=0) ^ (x v y=1)]=>y=x^'. The class of ...

A parallelogram (parallelepiped) containing the minimum repeatable elements of a circle (sphere) packing.

In one dimension, the interval [0,1] is the closed unit interval, the interval (0,1) is the open unit interval, and the intervals (0,1] and [0,1) are half-open unit intervals.

A point lattice which can be constructed from an arbitrary parallelogram of unit area. For any such planar lattice, the minimum distance c between any two points is a ...

The point in the plane with Cartesian coordinates (1, 1).

A sphere of radius 1.

An R-module M is said to be unital if R is a commutative ring with multiplicative identity 1=1_R and if 1m=m for all elements m in M.

Let A be a C^*-algebra, then two element a,b of A are called unitarily equivalent if there exists a unitary u in A such that b=uau^*.

An operator U satisfying U^|U = 1 (1) UU^| = 1, (2) where U^| is the adjoint.