field of sets

Complex - Mathematics. A complex number is a number in that field of numbers which includes the real numbers and the imaginary numbers, of the form a + ib, where a and b are real numbers and i is the imaginary number equal to the square root of -1. A complex is an element of a complex algebra or field of sets. A simplicial complex is a space that can be divided into fully adjacent triangles (more generally, simpl

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Elements of an interior algebra satisfying the condition xI = x are called open. The complements of open elements are called closed and are characterized by the condition xC = x. An interior of an element is always open and the closure of an element is always closed. Interiors of closed elements are called regular open and closures of open elements are called regular closed. Elements which are both ...

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Interior algebra, Interior algebra - Open and closed elements, Interior algebra - Morphisms of interior algebras, Interior algebra - Homomorphisms, Interior algebra - Topomorphisms, Interior algebra - Relationships to other areas of mathematics, Interior algebra - Topology, Interior algebra - Modal logic, Interior algebra - Preorders, Interior algebra - Monadic Boolean algebras, Interior algebra - Heyting algebras, Interior algebra - Derivative algebras

Read more here: » Interior algebra: Encyclopedia II - Interior algebra - Open and closed elements

Interior algebra - Homomorphisms. Since interior algebras are algebraic structures we can speak of interior algebra homomorphisms. Given two interior algebras A and B, a map f : A → B is an interior algebra homomorphism if and only if it is a homomorphism between the underlying Boolean algebras of A and B and in addition preserves interiors (and hence equivalently, preserves closures) i.e. f(xI) = f(x)I ...

See also:

Interior algebra, Interior algebra - Open and closed elements, Interior algebra - Morphisms of interior algebras, Interior algebra - Homomorphisms, Interior algebra - Topomorphisms, Interior algebra - Relationships to other areas of mathematics, Interior algebra - Topology, Interior algebra - Modal logic, Interior algebra - Preorders, Interior algebra - Monadic Boolean algebras, Interior algebra - Heyting algebras, Interior algebra - Derivative algebras

Read more here: » Interior algebra: Encyclopedia II - Interior algebra - Morphisms of interior algebras