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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...
We prove a separable reduction theorem for -porosity of Suslin sets. In particular, if is a Suslin subset in a Banach space , then each separable subspace of can be enlarged to a separable subspace such that is -porous in if and only if is -porous in . Such a result is proved for several types of -porosity. The proof is done using the method of elementary submodels, hence the results can be combined with other separable reduction theorems. As an application we extend a theorem...
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