A Note on Chains of Open Sets

A Note on Some Applications of Α-open Sets

The object of this note is to introduce and study topological properties of α-derived, α-border, α-frontier, and α-exterior of a set using the concept of α-open sets. Moreover, we study some further properties of the well-known notions of α-closure and α-interior. We also obtain a new decomposition of α-continuous functions. 1. Introduction. The notion of α-open set (originally called α-sets) i...

Some results on maximal open sets

In this paper, the notion of maximal m-open set is introduced and itsproperties are investigated. Some results about existence of maximal m-open setsare given. Moreover, the relations between maximal m-open sets in an m-spaceand maximal open sets in the corresponding generated topology are considered.Our results are supported by examples and counterexamples.

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.

A Note on Addition Chains

Abstract Addition chains give a very easy way of computing xn knowing x and n. The fact of having a minimal addition chain for an integer n gives the least number of multiplications needed to compute xn. In this paper, we will present the binary method which is optimal for any integer of Hamming weight 1 or 2. We will show that if n has k digits in its binary expansion and the minimal length of...

On Pre-θ-Open Sets and Two Classes of Functions