Displaying similar documents to “An answer to a question on hyperspaces”

Closed discrete subsets of separable spaces and relative versions of normality, countable paracompactness and property ( a )

Samuel Gomes da Silva (2011)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we show that a separable space cannot include closed discrete subsets which have the cardinality of the continuum and satisfy relative versions of any of the following topological properties: normality, countable paracompactness and property ( a ) . It follows that it is consistent that closed discrete subsets of a separable space X which are also relatively normal (relatively countably paracompact, relatively ( a ) ) in X are necessarily countable. There are, however, consistent...