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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 a chord of constant length be slid around a smooth, closed, convex curve C, and choose a point on the chord which divides it into segments of lengths p and q. This point ...

An axiom proposed by Huntington (1933) as part of his definition of a Boolean algebra, H(x,y)=!(!x v y) v !(!x v !y)=x, (1) where !x denotes NOT and x v y denotes OR. Taken ...

The invertible matrix theorem is a theorem in linear algebra which gives a series of equivalent conditions for an n×n square matrix A to have an inverse. In particular, A is ...

A theorem in the theory of univalent conformal mappings of families of domains on a Riemann surface, containing an inequality for the coefficients of the mapping functions, ...

Let L=(L, ^ , v ) and K=(K, ^ , v ) be lattices, and let h:L->K. If h is one-to-one and is a join-homomorphism, then it is a join-embedding.

Let L=(L, ^ , v ) and K=(K, ^ , v ) be lattices, and let h:L->K. If K=L and h is a join-homomorphism, then we call h a join-endomorphism.

Let L=(L, ^ , v ) and K=(K, ^ , v ) be lattices, and let h:L->K. Then the mapping h is a join-homomorphism provided that for any x,y in L, h(x v y)=h(x) v h(y). It is also ...

Let L=(L, ^ , v ) and K=(K, ^ , v ) be lattices, and let h:L->K. If h is one-to-one and onto, then it is a join-isomorphism if it preserves joins.

Kakutani's fixed point theorem is a result in functional analysis which establishes the existence of a common fixed point among a collection of maps defined on certain ...