Displaying similar documents to “Property ( a ) and dominating families”

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...

Almost disjoint families and property (a)

Paul Szeptycki, Jerry Vaughan (1998)

Fundamenta Mathematicae

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We consider the question: when does a Ψ-space satisfy property (a)? We show that if | A | < p then the Ψ-space Ψ(A) satisfies property (a), but in some Cohen models the negation of CH holds and every uncountable Ψ-space fails to satisfy property (a). We also show that in a model of Fleissner and Miller there exists a Ψ-space of cardinality p which has property (a). We extend a theorem of Matveev relating the existence of certain closed discrete subsets with the failure of property (a). ...

Spaces with large star cardinal number

Yan-Kui Song (2012)

Commentationes Mathematicae Universitatis Carolinae

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In this paper, we prove the following statements: (1) For any cardinal κ , there exists a Tychonoff star-Lindelöf space X such that a ( X ) ≥ κ . (2) There is a Tychonoff discretely star-Lindelöf space X such that a a ( X ) does not exist. (3) For any cardinal κ , there exists a Tychonoff pseudocompact σ -starcompact space X such that st - l ( X ) ≥ κ .

The G δ -topology and incompactness of ω α

Isaac Gorelic (1996)

Commentationes Mathematicae Universitatis Carolinae

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We establish a relation between covering properties (e.gĿindelöf degree) of two standard topological spaces (Lemmas 4 and 5). Some cardinal inequalities follow as easy corollaries.

The sup = max problem for the extent of generalized metric spaces

Yasushi Hirata, Yukinobu Yajima (2013)

Commentationes Mathematicae Universitatis Carolinae

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It looks not useful to study the sup = max problem for extent, because there are simple examples refuting the condition. On the other hand, the sup = max problem for Lindelöf degree does not occur at a glance, because Lindelöf degree is usually defined by not supremum but minimum. Nevertheless, in this paper, we discuss the sup = max problem for the extent of generalized metric spaces by combining the sup = max problem for the Lindelöf degree of these spaces.