Preserving continuity by Zadeh extension and invariance of separation axioms under surjections

Almost Gs-closed Functions and Separation Axioms

We introduce a new class of functions called almost gs-closed and use the functions to improve several preservation theorems of normality and regularity and also their generalizations. The main result of the paper is that normality and weak normality are preserved under almost gs-closed continuous surjections.

Generated topology on infinite sets by ultrafilters

Let $X$ be an infinite set, equipped with a topology $tau$. In this paper we studied the relationship between $tau$, and ultrafilters on $X$. We can discovered, among other thing, some relations of the Robinson's compactness theorem, continuity and the separation axioms. It is important also, aspects of communication between mathematical concepts.

Nash Bargaining without Scale Invariance

We present a characterization of the Nash Bargaining Solution on a domain which is not closed under Scale Invariance. The characterization on this restricted domain relies on Symmetry, Efficiency, Translation Invariance, the Independence of Irrelevant Alternatives and Continuity, but does not require Scale Invariance. Surprisingly, without continuity there exist a wide variety of bargaining sol...

Existence of Order-Preserving Functions for Nontotal Fuzzy Preference Relations under Decisiveness

Looking at decisiveness as crucial, we discuss the existence of an order-preserving function for the nontotal crisp preference relation naturally associated to a nontotal fuzzy preference relation. We further present conditions for the existence of an upper semicontinuous order-preserving function for a fuzzy binary relation on a crisp topological space.

On bD-Sets and Associated Separation Axioms