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In this paper we show that the set of all Koliha-Drazin invertible elements in a complex unital Banach algebra forms a regularity as defined by Kordula and Müller, and we explore the properties of the set as a regularity. We also use this result to simplify the proof that the set of all Drazin invertible elements of a complex unital Banach algebra forms a regularity. *doi:10.3318/pria.2007.107.2.137 fatcat:snuxztjo3zaq7de3g5zjqvciti