Main topic of the this work is to use the notion of unbounded convergences on vector lattices to derive properties of various classes of operators and nets of operators defined between vector lattices, Banach lattices, and ...

Order convergence and unbounded order convergence are not topological terms on Riesz space. On the other hand, compact operatör takes an important place in functional analysis. In this thesis, we investigate order compact ...

This thesis is partly based on recent developments on the subject of what is known as “injectivity domains” in the theory of modules over rings with identity. The subject was suggested as a measurement of how far a module ...

Let Σ be a closed orientable surface of genus at least 2 and Rep(Σ,G) be the smooth part of the representation variety of homomorphisms' conjugation classes from fundamental group of Σ to Lie group G. In this thesis, ...

he aim of this thesis is to make a compilation on the theory named as infinite combinatorialtopology or the selection principles in mathematics and to investigate the relations betweenthe sets of reals and Menger Conjecture.This ...

Let R be a commutative ring with identity and M_n(R) be the algebra (ring) of all n x n matrices over R. Note that an additive D of a ring R into itself is said to be a derivation of R if D(xy)=D(x)y+xD(y) for all x, y ...

A contact structure on an oriented three-manifold is a maximally non-integrable 2-plane field distributed all over the three-manifold. Legendrian knots and Legendrian links in contact three-manifolds give important ...

We study generalizations of the concept of direct-injectivity (respectively pure-direct-injectivity) from module categories to abelian categories (respectively Grothendieck categories). We examine for which categories or ...

The aim of this thesis is to explore the concept of frame, which is a special kind of a lattice, and to examine their topological properties, such as separation axioms and compactness. The study consists of six chapters. ...

In this thesis, a new structure-preserving numerical method for strongly coupled nonlinear Schrödinger equation (SCNLS) is presented. It is shown that the proposed new method conserves the discrete mass and energy. Numerical ...