arXiv subjects
Publications and source records attributed to Aliakbar Alijani.
In this paper, we study some properties of $*-$open and $*-$closed subsets of a space. The collection of all $*-$open subsets of a space $X$ form a topology on $X$ which is denoted by $^{*}O(X)$. We investigate the relations between topological properties of $X$ with the topology $^{*}O(X)$ and $X$. Also, we introduce the concept of a $*-$continuous map.
Let $\ell$ be the category of all locally compact abelian (LCA) groups. Let $G\in\ell$ and $H\subseteq G$. The first Ulm subgroup of $G$ is denoted by $G^{(1)}$ and the closure of $H$ by $\overline{H}$. A proper short exact sequence $0\to A\stackrelϕ{\to} B\stackrelψ{\to} C\to 0$ in $\ell$ is said to be a $TFU$ extension if $0\to \overline{A^{(1)}}\stackrel{\overlineϕ}{\to} \overline{B^{(1)}}\stackrel{\overlineψ}{\to} \overline{C^{(1)}}\to 0$ is a proper short exact sequence where $\overlineϕ=ϕ\mid_{\overline{A^{(1)}}}$ and $\overlineψ=ψ\mid_{\overline{B^{(1)}}}$. We introduce some results on $TFU$ extensions. Also, we establish conditions under which the $TFU$ extensions split.
A locally compact abelian group $G$ is called a generalized $\unicode{x00A3}$-cotosion group if $G$ contains an open $\unicode{x00A3}$-cotosion subgroup $H$ such that $G/H$ is a cotorsion group. In this paper, we determine the generalized $\unicode{x00A3}$-cotorsion LCA groups.
The aim of this paper is to introduce and give preliminary investigation of T-locally compact spaces. Locally compact and T-locally compact are independent of each other. Every Hausdorff, locally compact space is T-locally compact. T-locally compact is a topological property. T-locally compact is not preserved by the product topology.
Let G and C be two discrete abelian groups. It is known that Pext(C,G) is a subgroup of Ext(C,G). In this paper, we introduce the t-extensions of G by C. We will show that the set of all t-extensions of G by C is a subgroup of Ext(C,G) which contains Pext(C,G). Fulp and Griffith [4] determined the LCA groups G such that Ext(C,G)=0 for all compact connected groups C. Using the group of t-extensions, we determine the LCA groups G such that Pext(C,G)=0 for all compact connected groups C.