Small subsets of first countable spaces
Eric van Douwen, Michael Wage (1979)
Fundamenta Mathematicae
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Displaying similar documents to “A note on discrete sets”
Small subsets of first countable spaces
Property and dominating families
Samuel Gomes da Silva (2005)
Commentationes Mathematicae Universitatis Carolinae
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Generalizations of earlier negative results on Property are proved and two questions on an -version of Jones’ Lemma are posed. We discuss these questions in the realm of locally compact spaces. Using dominating families of functions as a tool, we prove that under the assumptions “ is regular” and “” the existence of a separable locally compact -space with an uncountable closed discrete subset implies the existence of inner models with measurable cardinals. We also use cardinal...
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.