This article is cited in 8 papers

On the cardinality of compactifications of dyadic spaces

B. A. Efimov


Abstract: It is shown that the supercardinality of a completely regular space $X$ equivalent to a dyadic space is equal to $\exp(\pi wX)$ provided $(\pi wX)^{\omega_0}=\pi wX$, where $\pi wX$ is the $\pi$-weight of $X$. In particular, it follows that the supercardinality of any countable dense subspace of a dyadic compactum of weight $\exp\omega_0$ is equal to $\exp\exp\omega_0$. This solves a problem raised by A. V. Arkhangel'skii on whether there exists a countable completely regular space whose every compactification has a cardinality larger than the continuum.
Bibliography: 12 titles.

UDC: 513.83

MSC: Primary 54A25, 54D35; Secondary 54D15

Received: 28.06.1974

 English version: Mathematics of the USSR-Sbornik, 1975, 25:4, 579–593

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