The Minimal Structures and Continuous Multifunctions in Bi-m-spaces

Minimal Structures and Continuous Multifunctions in Bi-m-spaces

Abstract

 Let (X, m1 X, m2 X) be a bi-minimal space and F : (X, m1 X, m2 X) → (Y, m1 Y , m2 Y ) be a multifunction. The purpose of this paper is to obtain properties of the multifunction F. For the purpose, we define a unified form Mij X (resp. Mij Y ) of several minimal structures on (X, m1 X, m2 X) (resp. (Y, m1 Y , m2 Y ) ) and investigate properties of an Mij -continuous multifunction F : (X, Mij X ) → (Y, Mij Y ). As a special case, we obtain some properties of upper and lower (τ1, τ2)-precontinuous multifunction F : (X, τ1, τ2) → (Y, σ1, σ2) [3].