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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Two results concerning cardinal functions on compact spaces
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by I. Juhász and Z. Szentmiklóssy PDF
Proc. Amer. Math. Soc. 90 (1984), 608-610 Request permission

Abstract:

We show that for $X$ compact ${T_2}:\left ( i \right )d\left ( X \right ) \leqslant s\left ( X \right ) \cdot \hat F\left ( X \right )$; (ii) if the pair $\left ( {\kappa ,\hat F\left ( X \right )} \right )$ is a caliber of $X$ then $\pi \left ( X \right ) < \kappa$. These strengthen results of Šapirovskii from [3 and 5], respectively. Moreover, (i) settles a problem raised in [2] implying that there are no compact ${T_2}$ $\kappa$-examples for any singular cardinal $\kappa$.
References
    I. Juhász, Cardinal functions in topology—ten years later, Math. Centre Tracts, Vol. 123, Math. Centrum, Amsterdam, 1980.
  • I. Juhász and W. Weiss, The determination of $\pi$-weight by subspaces of singular cardinality, C. R. Math. Rep. Acad. Sci. Canada 3 (1981), no. 5, 257–260. MR 630941
  • B. Šapirovskii, Canonical sets and character. Density and weight in compact spaces, Soviet Math. Dokl. 15 (1974), 1282-1287. —, Special types of embeddings in Tychonoff cubes. Subspaces of $\Sigma$-products and cardinal invariants, Topology, Vol. II (Proc. Fourth Colloq., Budapest, 1978), Colloq. Math. Soc. János Bolyai, Vol. 23, North-Holland, Amsterdam, 1980, pp. 1055-1086.
  • B. È. Shapirovskiĭ, Cardinal invariants in compacta, Seminar on General Topology, Moskov. Gos. Univ., Moscow, 1981, pp. 162–187 (Russian). MR 656957
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Additional Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 90 (1984), 608-610
  • MSC: Primary 54A25; Secondary 54D30
  • DOI: https://doi.org/10.1090/S0002-9939-1984-0733414-1
  • MathSciNet review: 733414