A topological version of $\diamondsuit$
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- by John Ginsburg
- Proc. Amer. Math. Soc. 65 (1977), 142-144
- DOI: https://doi.org/10.1090/S0002-9939-1977-0441737-5
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Abstract:
The set-theoretic principle $\diamondsuit$ is shown to be equivalent to the existence of universal ${\omega _1}$-sequences in certain topological spaces. An ${\omega _1}$-sequence $({x_\alpha }:\alpha \in {\omega _1})$ in a space X is said to be universal in X if for every point $p \in X$ there is a stationary set $S \subseteq {\omega _1}$ so that the net $({x_\alpha }:\alpha \in S)$ converges to p. It is shown that the existence of universal ${\omega _1}$-sequences in spaces of weight $\leqslant c$ is equivalent to $\diamondsuit$.References
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Bibliographic Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 65 (1977), 142-144
- MSC: Primary 04A20; Secondary 54A20, 54A25
- DOI: https://doi.org/10.1090/S0002-9939-1977-0441737-5
- MathSciNet review: 0441737