cozero maps are generalized forms of cozero elements. two particular cases of cozero maps, slim and regular cozero maps, are significant. in this paper we present methods to construct slim and regular cozero maps from a given  cozero map. the construction of the slim and the regular cozero map from a cozero map are called slimming and regularization of the cozero map, respectively. also, we pro...

In this note we shall characterize a topological property which is stronger than countable paracompactness but which is equivalent to it for normal spaces. A real valued function on a topological space X is locally bounded if each point has a neighborhood on which the function is bounded. Let C(X) denote the set of real valued continuous functions on X. A topological space is a cb-space if for ...

Let R be a commutative ring with non-zero identity. The cozero-divisor graph of R, denoted by , is a graph with vertices in   R     W R  , which is the set of all non-zero and non-unit elements of R, and two distinct vertices a and b in are adjacent if and only if and   W R  a bR  b aR  . In this paper, we investigate some combinatorial properties of the cozero-divisor graphs    ...

Let R be a commutative ring with non-zero identity. The cozero-divisor graph of R, denoted by Γ′(R), is a graph with vertices in W ∗(R), which is the set of all non-zero and non-unit elements of R, and two distinct vertices a and b in W ∗(R) are adjacent if and only if a / ∈ bR and b / ∈ aR. In this paper, we characterize all commutative rings whose cozero-divisor graphs are forest, star, doubl...

In [1], Afkhami and Khashyarmanesh introduced the cozero-divisor graph of a ring, Γ′(R), which examines relationships between principal ideals. We continue investigating the algebraic implications of the graph by developing the reduced cozero-divisor graph, which is a simpler analog. Acknowledgements: This research was undertaken at the Wabash College Mathematics REU in Crawfordsville, Indiana....

This paper is concerned with solvability and solution stability of parametric generalized equations governed by set-valued mappings. By a degree-theoretic approach for multifunctions, some new results on lower semicontinuity of the solution map to a parametric generalized equation are established.

Let X be a locally compact Hausdorff space and C0(X) the Banach space of continuous functions on X vanishing at infinity. In this paper, we shall study unbounded disjointness preserving linear functionals on C0(X). They arise from prime ideals of C0(X), and we translate it into the cozero set ideal setting. In particular, every unbounded disjointness preserving linear functional of c0 can be co...