arXiv subjects
Publications and source records attributed to Abdullah Aydın.
Let $(E,τ)$ be a locally solid vector lattice. A filter $\mathcal{F}$ on the set $E$ is said to be converge to a vector $e\in E$ if, each zero neighborhood set $U$ containing $e$, $U$ belongs to $\mathcal{F}$. We study on the concept of this convergence and give some basic properties of it.
Let $X$ be a vector lattice and $(E,τ)$ be a locally solid vector lattice. An operator $T:X\to E$ is said to be $ob$-bounded if, for each order bounded set $B$ in $X$, $T(B)$ is topologically bounded in $E$. In this paper, we study on algebraic properties of $ob$-bounded operators with respect to the topology of uniform convergence and equicontinuous convergence.