UPPER AND LOWER $(I,J)$-CONTINUOUS MULTIFUNCTIONS

J Moreno,E Rosas,C Carpintero

doi:10.12732/ijpam.v117i1.9

Abstract

UPPER AND LOWER $(I,J)$-CONTINUOUS MULTIFUNCTIONS

Highlights

It is well known today, that the notion of multifunction is playing a very impor-Received: A2017-06-09Revised: Published: November 28, 2017§Correspondence author c 2017 Academic Publications, Ltd. url: www.acadpubl.euE
Moreno tant role in general topology, upper and lower continuity have been extensively studied on multifunctions F : (X, τ ) → (Y, σ)
In 1990, Jankovic and Hamlett [10], introduced the notion of I-open set in a topological space (X, τ ) with an ideal I on X

Summary

Introduction

It is well known today, that the notion of multifunction is playing a very impor-. E. Using the notion of topological ideal, different types of upper and lower continuity in multifunction F : (X, τ, I) → (Y, σ) have been studied and characterized [2], [8], [9], [14], [17]. In 1990, Jankovic and Hamlett [10], introduced the notion of I-open set in a topological space (X, τ ) with an ideal I on X. In 2007, Akdag [2], introduce the concept of I-continuous multifunctions in a topological space with and ideal on it. We introduce and study a new class of multifunction called a nearly (I, J)-continuous multifunctions in topological spaces. Investigate its relation with another class of continuous multifunctions We introduce another types of (I, J)-continuous multifunctions

Preliminaries

Upper and Lower Nearly I-Continuous Multifunctions