In this paper, we discuss the Maxwell equations in terms of differential forms, both in the 3-dimensional space and in the 4-dimensional space-time manifold. Further, we view the classical electrodynamics as the curvature of a line bundle, and fit it into gauge theory.
In this article we investigate the notion and basic properties of Boolean algebras and prove the Stones representation theorem. The relations of Boolean algebras to logic and to set theory will be studied and, in particular, a neat proof of completen
ess theorem in propositional logic will be given using Stones theorem from Boolean algebra.
In this article, we shall explore the constructions of Bernstein sets, and prove that every Bernstein set is nonmeasurable and doesnt have the property of Baire. We shall also prove that Bernstein sets dont have the perfect set property.
In this article, the author proposes another way to define the completion of a metric space, which is different from the classical one via the dense property, and prove the equivalence between two definitions. This definition is based on consideratio
ns from category theory, and can be generalized to arbitrary categories.
