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, ...

Let $R$ be a commutative ring with identity and $G=(V,E)$ be a finite graph, where $V$ is a set of elements of vertices and $E$ is a set of elements of edges. A map $ \alpha : E \to \{\text{ideals in R}\}$ is called ...