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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Cardinal functions for $ k$-spaces

Authors: James R. Boone, Sheldon W. Davis and Gary Gruenhage
Journal: Proc. Amer. Math. Soc. 68 (1978), 355-358
MSC: Primary 54D50; Secondary 54A25
MathSciNet review: 0467676
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Abstract: In this paper, four cardinal functions are defined on the class of k-spaces. Some of the relationships between these cardinal functions are studied. Characterizations of various k-spaces are presented in terms of the existence of these cardinal functions. A bound for the ordinal invariant $ \kappa $ of Arhangelskii and Franklin is established in terms of the tightness of the space. Examples are presented which exhibit the interaction between these cardinal invariants and the ordinal invariants of Arhangelskii and Franklin.

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Keywords: Cardinal function, ordinal invariant, k-space
Article copyright: © Copyright 1978 American Mathematical Society