Jiling Cao, Department of Mathematics, The University of Auckland, Private Bag 92019, Auckland, New Zealand. e-mail: firstname.lastname@example.org; Ivan L. Reilly, School of Mathematical & Information Sciences, The University of Auckland, Private Bag 92019, Auckland, New Zealand. e-mail: email@example.com
Abstract: Recently Popa and Noiri  established some new characterizations and basic properties of $\alpha$-continuous multifunctions. In this paper, we improve some of their results and examine further properties of $\alpha$-continuous and $\alpha$-irresolute multifunctions. We also make corrections to some theorems of Neubrunn .
Keywords: upper (lower) $\alpha$-continuous, upper (lower) $\alpha$-irresolute, strongly $\alpha$-closed graph, almost compact, almost paracompact
Classification (MSC 1991): 54C60, 54E55
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