Transformations Depending on Sets of Associated 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.

On the existence of fixed points for contraction mappings‎ ‎depending on two functions

‎In this paper we study the existence of fixed points for mappings defined on complete metric spaces‎, ‎satisfying a general contractive inequality depending on two additional mappings‎.

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

On Transformations with Invariant Points* By

1. There is a well known theorem by Brouwer f to the effect that every sensepreserving transformation of a spherical surface into itself such that both the direct transformation and its inverse are one-valued leaves invariant at least one point of the surface. It is proposed to prove a somewhat more general theorem by a simplified process and to outline one or two applications of the theorem in...