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There are at least two distinct (though related) notions of the term Hilbert algebra in functional analysis. In some literature, a linear manifold A of a (not necessarily ...

Let X=(X,tau) be a topological vector space whose continuous dual X^* may or may not separate points (i.e., may or may not be T2). The weak-* (pronounced "weak star") ...

Let s_i be the orders of singular points on a curve (Coolidge 1959, p. 56). Harnack's first theorem states that a real irreducible curve of order n cannot have more than ...

A bounded lattice is an algebraic structure L=(L, ^ , v ,0,1), such that (L, ^ , v ) is a lattice, and the constants 0,1 in L satisfy the following: 1. for all x in L, x ^ ...

A rooted graph is a graph in which one node is labeled in a special way so as to distinguish it from other nodes. The special node is called the root of the graph. The rooted ...

A transcendental number is a (possibly complex) number that is not the root of any integer polynomial, meaning that it is not an algebraic number of any degree. Every real ...

The pure equation x^p=C of prime degree p is irreducible over a field when C is a number of the field but not the pth power of an element of the field. Jeffreys and Jeffreys ...

A semigroup S is said to be an inverse semigroup if, for every a in S, there is a unique b (called the inverse of a) such that a=aba and b=bab. This is equivalent to the ...

An iterated map is a map that is applied repeatedly to an object. The Wolfram Language function NestList[f, expr, n] gives a list of the results of iterating the function f n ...

Let I be a set, and let U be an ultrafilter on I, let phi be a formula of a given language L, and let {A_i:i in I} be any collection of structures which is indexed by the set ...