A Remark on a problem of Mrówka

Recently Mrówka 7] defined nearly-Lindelöf spaces (see Definition 2.1) and asked the following question: Is every nearly-Lindelof space a Lindelöf space? We will answer this question positively (see Corollary 2.5). However we will first prove some results concerning the related concepts of a, b]-compactness (see Definitions 3.1 and 3.2) of topological spaces, from which the answer to Mrówka’s question will immediately follow.