Domain Theory In Math

The preceding theory was the so called domain theory that considers uniformly magnetized domains separated by magnetic walls of zero thickness with a number of rules concerning the orientation of the magnetization in the domains and of the domain walls dws hereafter.

Domain theory in math. The field has major applications in computer science where it is used to specify denotational semantics especially for functional programming languages. In topology a domain is a connected open set. In the study of partial differential equations a domain is the open connected subset of the euclidean space where a problem is posed i e where the unknown.

In micromagnetics domains and walls are all described by a continuous function the local magnetization a classical vector that is the local average over a small volume of the magnetization density. Domain theory formalizes the intuitive ideas of approximation and convergence in a very general way and is closely related to topology. Domain theory is a branch of mathematics that studies special kinds of partially ordered sets posets commonly called domains.

Another way of looking at domain theory is to say that it is a way of modelling the fact that certain computations don t have a defined result and using the model to prove that certain computations will ultimately provide as close to a complete definition as we could demand.