On Some Generalized Compactness Properties

Since Dieudonne [3] first defined paracompactness in 1944, various authors have introduced, studied and related to one another a number of properties similar in description to paracompactness. Examples are metacompactness [1], hypocompactness [9], countable paracompactness [4] and countable metacompactness [6]. The purpose of this paper is to present some examples which clarify the extent to which Hausdorff spaces with various combinations of these properties can exist. Since terminology varies considerably in the literature, some preliminary definitions are advisable. Terms not defined herein may be found in [5].