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For every topological property , we define the class of -approximable spaces which consists of spaces X having a countable closed cover such that the “section” has the property for each . It is shown that every -approximable compact space has , if is one of the following properties: countable tightness, -scatteredness with respect to character, -closedness, sequentiality (the last holds under MA or ). Metrizable-approximable spaces are studied: every compact space in this class has...
A subset of a Hausdorff space is called an H-set in if for every open family in such that there exists a countable subfamily of such that . In this paper we introduce a new cardinal function and show that for every H-set of a Hausdorff space .
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