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Proceedings of the American Mathematical Society

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Having a small weight is determined by the small subspaces


Authors: A. Hajnal and I. Juhász
Journal: Proc. Amer. Math. Soc. 79 (1980), 657-658
MSC: Primary 54A25
MathSciNet review: 572322
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Abstract: We show that for every cardinal $ \kappa > \omega $ and an arbitrary topological space X if we have $ w(Y) < \kappa $ whenever $ Y \subset X$ and $ \vert Y\vert \leqslant \kappa $ then $ w(X) < \kappa $ as well. M. G. Tkačenko proved this for $ {T_3}$ spaces in [2]. We also prove an analogous statement for the $ \pi $-weight if $ \kappa $ is regular.


References [Enhancements On Off] (What's this?)

  • [1] I. Juhász, Cardinal functions in topology, Mathematisch Centrum, Amsterdam, 1971. In collaboration with A. Verbeek and N. S. Kroonenberg; Mathematical Centre Tracts, No. 34. MR 0340021
  • [2] M. G. Tkačenko, Chains and cardinals, Dokl. Akad. Nauk SSSR 239 (1978), no. 3, 546–549 (Russian). MR 0500798

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1980-0572322-2
Keywords: Weight ($ \pi $-weight) of a topological space
Article copyright: © Copyright 1980 American Mathematical Society