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It is well known that for a Hausdorff topological group $X$, the limits of convergent sequences in $X$ define a function denoted by $\lim$ from the set of all convergent sequences in $X$ to $X$. This notion has been modified by Connor and Grosse-Erdmann for real functions by replacing $\lim$ with an arbitrary linear functional $G$ defined on a linear subspace of the vector space of all real sequences. Recently some authors have extended the concept to the topological group setting and introduced the concepts of $G$-continuity, $G$-compactness and $G$-connectedness. In this paper we prove some results on different types of $G$-compactness for topological group with operations which include topological groups, topological rings without identity, R-modules, Lie algebras, Jordan algebras, and many others., Comment: 14 pages, Research paper

In this paper, we introduce a concept of a soft matrix on a soft multiset, and investigate how to use soft matrices to solve decision making problems. An algorithm for a multiple choose selection problem is also provided. Finally, we demonstrate an illustrative example to show the decision making steps., Comment: 16 pages

In this paper, we introduce soft continuous mappings which are defined over an initial universe set with a fixed set of parameters. Later we study soft open and soft closed mappings, soft homeomorphism and investigate some properties of these concepts., Comment: 12 pages

Recently, Cakalli has introduced a concept of $G$-sequential connectedness in the sense that a non-empty subset $A$ of a Hausdorff topological group $X$ is $G$-sequentially connected if there are no non-empty, disjoint $G$-sequentially closed subsets $U$ and $V$ meeting $A$ such that $A\subseteq U\bigcup V$. In this paper we investigate further properties of $G$-sequential connectedness and prove some interesting theorems., Comment: 11 pages, Research paper. arXiv admin note: substantial text overlap with arXiv:1105.2203

The main object of this paper is to investigate lacunary statistically ward continuity. We obtain some relations between this kind of continuity and some other kinds of continuities. It turns out that any lacunary statistically ward continuous real valued function on a lacunary statistically ward compact subset $E\subset{\textbf{R}}$ is uniformly continuous., Comment: 20 pages