First order conditions are given which are necessary for a commutative regular ring to have a prime integrally closed extension. If the ring is countable these conditions are also sufficient. In [8] an example was given of a commutative regular ring with no prime model extension to a commutative integrally closed regular ring. In this paper we give (in §2) first order conditions which are neces...

The primary goal is to characterize Locally H-closed spaces (LHC), by conditions on the remainders of their extensions. These are also characterized using subspaces and extensions as well. Characterizing these classes in provide characterizations them terms boundaries. Recently, authors have proved that results give necessary sufficient for space be compact A number equivalences Hausdorff (Urys...

In this paper we introduce intuitionistic fuzzy contra regular weakly generalized open mappings and intuitionistic fuzzy contra regular weakly generalized closed mappings. We investigate some of their properties.

We show that if the intersection number c2 > 1 then any weak-geodetically closed subgraph of X is distance-regular. Γ is said to be i-bounded, whenever for all x, y ∈ X at distance δ(x, y) ≤ i, x, y are contained in a common weakgeodetically closed subgraph of Γ of diameter δ(x, y). By a parallelogram of length i, we mean a 4-tuple xyzw of vertices in X such that δ(x, y) = δ(z, w) = 1, δ(x,w) =...

For a closure space (P,φ) with φ(∅) = ∅, the closures of open subsets of P , called the regular closed subsets, form an ortholattice Reg(P,φ), extending the poset Clop(P,φ) of all clopen subsets. If (P,φ) is a finite convex geometry, then Reg(P, φ) is pseudocomplemented. The Dedekind-MacNeille completion of the poset of regions of any central hyperplane arrangement can be obtained in this way, ...

With progressing technologies and new features of production, new products compete with older ones in markets. Indeed, new products initiate contest with olden ones and this process repeats in different productions lifetime several times. In this situation recycling the olden products seems to be significant for supply chains. Governments often levy special tariffs for these products as a contr...

Copyright c © 2013 Varun Joshi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract The aim of this paper is to introduce and study gprw-closed and gprw-quasi closed functions in topological spaces. Also some properties...

A subset A of a space X is called regular open if A = IntA, and regular closed if X\A is regular open, or equivalently, if A= IntA. A is called semiopen [16] (resp., preopen [17], semi-preopen [3], b-open [4]) ifA⊂ IntA (resp.,A⊂ IntA,A⊂ IntA ,A⊂ IntA∪ IntA). The concept of a preopen set was introduced in [6] where the term locally dense was used and the concept of a semi-preopen set was introd...

Let be a distance-regular graph of diameter d, valency k and r := max{i | (ci , bi ) = (c1, b1)}. Let q be an integer with r + 1 ≤ q ≤ d − 1. In this paper we prove the following results: Theorem 1 Suppose for any pair of vertices at distance q there exists a strongly closed subgraph of diameter q containing them. Then for any integer i with 1 ≤ i ≤ q and for any pair of vertices at distance i ...

Let Γ be a distance-regular graph of diameter d , and t be an integer with 2 ≤ t ≤ d − 1 such that at−1 = 0. For any pair (u, v) of vertices, let Π (u, v) be the subgraph induced by the vertices lying on shortest paths between u and v. We prove that if Π (u, v) is a bipartite geodetically closed subgraph for some pair (u, v) of vertices at distance t , then Π (x, y) is a bipartite geodetically ...