Continuity and Context

Automatic Continuity in Associative and Nonassociative Context

There are excellent accounts on automatic continuity theory in the associative context. Since there have been a number of advances in automatic continuity theory in the nonassociative context, it seems to be an opportune time to present a comprehensive discussion of the currently known results on automatic continuity of linear maps in this context. These notes are an attempt to collect together...

Business Continuity Management The Concept and Context of BCM

Density Continuity Versus Continuity

Real-valued functions of a real variable which are continuous with respect to the density topology on both the domain and the range are called density continuous. A typical continuous function is nowhere density continuous. The same is true of a typical homeomorphism of the real line. A subset of the real line is the set of points of discontinuity of a density continuous function if and only if...

L-FUZZY BILINEAR OPERATOR AND ITS CONTINUITY

The purpose of this paper is to introduce the concept of L-fuzzybilinear operators. We obtain a decomposition theorem for L-fuzzy bilinearoperators and then prove that a L-fuzzy bilinear operator is the same as apowerset operator for the variable-basis introduced by S.E.Rodabaugh (1991).Finally we discuss the continuity of L-fuzzy bilinear operators.

Join-continuity + Hypercontinuity = Prime continuity

Abstract. A remarkable result due to Kou, Liu & Luo states that the condition of continuity for a dcpo can be split into quasi-continuity and meet-continuity. Their argument contained a gap, however, which is probably why the authors of the monograph Continuous Lattices and Domains used a different (and fairly sophisticated) sequence of lemmas in order to establish the result. In this note we s...