-approximable compact spaces
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...