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A commutative group.

A point which is a member of the set closure of a given set S and the set closure of its complement set.

The curve given by the polar equation r=a(1-cos t). It resembles a heart.

When finite, the number of vectors in a basis for the vector space.

Also known as the totient function, it returns the number of positive integers which share a divisor with the input.

A commutative division ring.

A locally length-minimizing curve.

Also known as complex analytic, this type of function satisfies the Cauchy-Riemann equations.

A point p which is a member of a set A such that there is an open subset U of A containing p.

A particular Laurent polynomial associated to a knot.

The unique group of order 4 which is not cyclic.

A function f such that |f(x)-f(y)| < = L|x-y| for all x and y, where L is a constant independent of x and y.

A topological space that is Hausdorff, second countable, and locally Euclidean.

A property of a subgroup H of G where gHg^-1 = H for every g in G.

A type of matrix whose transpose is equal to its inverse.

A type of ideal I where if ab is in I then either a or b is in I.

The group consisting of all equivalence classes of cosets of a normal subgroup.

An algebraic structure, some examples including polynomials over Z, matrices over R, and the integers modulo n.

A name for the group of permutations.

The mathematical study of the properties that are preserved through deformations, twistings, and stretchings of objects.

An type of infinite set X for which there is no bijection between X and the integers.

A location where two or more lines or edges meet.

A type of set having the property that every subset has a least element.

A three-dimensional embedding such that every axis-parallel line contains either zero or two vertices.

If 1/p + 1/q = 1, p>1, a>=0, b>=0 then a^p/p + b^q/q >= ab.

A nonzero ring element x such that xy = 0 for some y in the ring.

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