A weak form of some types of continuous multifunctions

Abstract

Abstract. The aim of this paper is to introduce and study upper and lower almost γ-continuous multifunctions as a generalization of some types of continuous multifunctions including almost continuity, almost α-continuity, almost precontinuity, almost quasi-continuity and γ-continuity. Furthermore, basic characterizations, preservation theorems and several properties concerning upper and lower almost γ-continuous multifunctions are investigated. The relationships between almost γ-continuous multifunctions and the other types of continuity are also discussed.

On Set-Valued Mappings

“…In this section, we discuss and prove some results on the concept of U/L. δ-m-pre-continuous, we begin with the following four theorems which due to the E. Ekici [40], that he collect many of important basic terms for the generalize forms of SV-map. In the end of this section we state and prove the following four theorems, but in beigen we need to the following lemma, 5-3) Lemma: [112], For a SV-map F :XY, and any subsets AX, BY, the following assertions hold:…”

Upper and Lower almost $(\tau_1,\tau_2)$-continuous Multifunctions

“…Some characterizations of upper and lower almost β-continuous multifunctions were investigated in [25]. In 2006, Ekici and Park [11] introduced and studied almost γ-continuous multifunctions. Noiri and Popa [21] introduced and investigated the notions of upper and lower almost m-continuous multifunctions as multifunctions from a set satisfying some minimal conditions into a topological space.…”

Upper and Lower almost Weak (Ï„1, Ï„2)-continuity

“…Smithson [27] and Popa [23,24] extended independently these concepts to multifunctions by introducing and characterizing the notions of almost continuous multifunctions and weakly continuous multifunctions. Ekici and Park [9] introduced and studied upper and lower almost γ-continuous multifunctions as a generalization of some types of continuous multifunctions including almost continuity, almost α-continuity, almost precontinuity, almost quasi-continuity and γ-continuity. The concept of bitopological spaces was first introduced by Kelly [14].…”