Associated Sets of Points

Some points on generalized open sets

The paper is an attempt to represent a study of limit points, boundary points, exterior points, border, interior points and closure points in the common generalized topological space. This paper takes a look at the possibilities of an extended topological space and it also considers the new characterizations of dense set.

Inductive construction of self-associated sets of points

In 1889, Castelnuovo [Ca1] showed that if P1, . . . , P2r+2 are 2r + 2 self-associated points in linearly general position in IP , not lying on a rational normal curve of degree r, then the (r − 2)-plane of IP , spanned by any r − 1 of them and denoted by Λ, is an (r− 1)-secant plane to the unique rational normal curve of degree r, say C , through the remaining r + 3 points. Moreover, the inter...

On Self-associated Sets of Points in Small Projective Spaces

We study moduli of “self-associated” sets of points in P for small n. In particular, we show that for n = 5 a general such set arises as a hyperplane section of the Lagrangean Grassmanian LG(5, 10) ⊂ P (this was conjectured by Eisenbud-Popescu in Geometry of the Gale transform, J. Algebra 230); for n = 6, a general such set arises as a hyperplane section of the Grassmanian G(2, 6) ⊂ P. We also ...

On bD-Sets and Associated Separation Axioms

INDEPENDENT SETS OF SOME GRAPHS ASSOCIATED TO COMMUTATIVE RINGS

Let $G=(V,E)$ be a simple graph. A set $Ssubseteq V$ isindependent set of $G$,  if no two vertices of $S$ are adjacent.The  independence number $alpha(G)$ is the size of a maximumindependent set in the graph. In this paper we study and characterize the independent sets ofthe zero-divisor graph $Gamma(R)$ and ideal-based zero-divisor graph $Gamma_I(R)$of a commutative ring $R$.