Some Properties of -open Sets
A coating for improved resistance welding of galvanized steel parts or sheets comprises a binder, and a metal phosphide pigment, preferably a ferrophosphorus pigment, having a particle size of from about 0.1 to about 30 microns. The pigment can also include up to about 40% by weight of an additional metal such as tin, aluminum or lead, which can be combined with the metal phosphide in pigment form or deposited onto the surface of the particles. The coating can be applied to either the faying or non-faying surfaces of the galvanized steel, or to the resistance welding electrode, and may be removed, if desired, after the welding operation. The advantages of the present invention include a significant reduction in welding current and an increase in the weldability lobe width, a restoration of the dynamic resistance beta peak, and an increase in electrode life.
Weak and strong forms of β-irresolute functions
A subset A of a topological space X is said to be β-open [1] if A ⊂ Cl (Int (Cl (A))). A function f : X → Y is said to be β-irresolute [4] if for every β-open set V of Y, f-1(V) is β-open in X. In this paper we introduce weak and strong forms of β-irresolute functions and obtain several basic properties of such functions.
S-SETS AND COS-CLOSED TOPOLOGIES
In 1963, Levine [8] introduced and studied the concept of semi-open sets in topological spaces. In 1976, Thompson [13] used semi-open sets to define the class of S-closed spaces. In his own study of S-closed spaces, Noiri [9] investigated certain subsets of a given topological space (X, τ) which he called S-closed relative to (X, τ) . Di Maio [1] , calling such subsets S-sets, observed that in any space (X, τ) the family of open sets whose complements are S-sets forms a base for a coarser topology τ ∗ on X . In [1] this topology was used to define and study so-called S-continuous functions between topological spaces. Quite recently, Jiang and Reilly [6] extended Di Maio’s work on S-continuity, and they called the associated topology τ ∗ the co-S-closed topology of the space (X, τ) . The purpose of this paper is to discuss in greater detail the concept of co-S-closed topologies. We will start with various results about S-sets in topological spaces and then move