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Abstract
This paper continues the study of set-valued functions. It introduces notions of generalized openness for multifunctions, and establishes some of their basic properties and characterizations.
Abstract
The aim of this paper is to introduce two kinds of generalized continuity for multifunctions. Basic properties and characterizations of such multifunctions are established. These two generalized continuities include many of the variations of multifunction continuity already in the literature as special cases.
Abstract
Recently the class of clopen continuous functions between topological spaces has been generalized by the definition of the class of almost clopen continuous functions. The aim of this paper is to reconsider this second class of functions from the perspective of change of topology. Indeed, we show that the concept of almost clopen continuity coincides with the classical notion of continuity provided that suitable changes are made to the topologies of the domain and codomain of the function. We investigate some of the consequences of this situation.
Abstract
Let X and Y be compact Hausdorff spaces, and let E be a Banach lattice. In this short note, we show that if there exists a Riesz isomorphismΦ:C(X, E) →C(Y, R) such that Φ(f) has no zeros if f has none, then X is homeomorphic to Y and E is Riesz isomorphic to R.
