The finite topology and variational calculus on nontopological vector spaces

compactifications and function spaces on weighted semigruops

chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...

Topology on locally finite metric spaces

The necessity of a theory of General Topology and, most of all, of Algebraic Topology on locally finite metric spaces comes from many areas of research in both Applied and Pure Mathematics: Molecular Biology, Mathematical Chemistry, Computer Science, Topological Graph Theory and Metric Geometry. In this paper we propose the basic notions of such a theory and some applications: we replace the cl...

On Partitions of Finite vector Spaces

In this note, we give a new necessary condition for the existence of non-trivial partitions of a finite vector space. Precisely, we prove that the number of the subspaces of minimum dimension t of a non-trivial partition of Vn(q) is greater than or equal to q + t. Moreover, we give some extensions of a well known Beutelspacher-Heden’s result on existence of T -partitions.

Topology of a Nontopological Magnetic Monopole

Certain nontopological magnetic monopoles, recently found by Lee and Weinberg, are reinterpreted as topological solitons of a non-Abelian gauged Higgs model. Our study makes the nature of the Lee-Weinberg monopoles more transparent, especially with regard to their singularity structure. Submitted to Physics Letters B. e-mail address: [email protected] Address after Sept. 1, 1994: Physic...

Vector Calculus and the Topology of Domains in 3-Space