On Upper and Lower Almost ⍺-Continuous Multifunctions

A weak form of some types of continuous multifunctions

“…Upper almost continuous [24] (resp. upper almost α-continuous [30], upper almost quasi-continuous [19,29], upper almost precontinuous [31], upper almost β-continuous [20,32]…”

“…We give examples for the last three implications as follows. The other examples can be obtained in [19,24,29,30,31]. …”

“…Many different forms of continuous multifunctions have been introduced over the years. Some of them are semi-continuity [22], α-continuity [16], precontinuity [26], quasi-continuity [25], γ-continuity [2] and δ-precontinuity [21]. 1 The purpose of this paper is to give a new weaker form of some types of continuity including almost continuity [24], almost α-continuity [30], almost precontinuity [31], almost quasi-continuity [19,29] and γ-continuity.…”

Characterizations of upper and lower \alpha(\mu_X,\mu_Y)-continuous multifunctions

“…Some of them are semi-continuity [22], α-continuity [17], precontinuity [24], quasi-continuity [23], γ-continuity [2] and δ-precontinuity [21]. Most of these weaker forms of continuity, in ordinary topology such as α-continuity and β-continuity, have been extended to multifunctions [20,[25][26][27][28]. Császár [5] introduced the notions of generalized topological spaces and generalized neighbourhood systems.…”

On S-Precontinuous Multifunctions

“…In 1978, Smithson [16] and Popa [12] introduced independently the concept of almost continuous multifunctions (in the sense of Husain) in topological spaces. In 1988, Popa [13] introduced the notion of precontinuous multifunctions and showed that ii-almost continuity and precontinuity are equivalent for multifunctions.…”