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A closed separable subspace of $ \beta{\bf N}$ which is not a retract


Author: Petr Simon
Journal: Trans. Amer. Math. Soc. 299 (1987), 641-655
MSC: Primary 54G20; Secondary 04A20, 54D35
DOI: https://doi.org/10.1090/S0002-9947-1987-0869226-5
MathSciNet review: 869226
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Abstract: We shall exhibit a countable subset, $ X$, of $ {{\mathbf{N}}^{\ast}}$ whose closure is not a retract of $ \beta {\mathbf{N}}$. The points of $ X$ are constructed in $ c$ steps with the aid of an independent matrix of subsets of $ \omega $.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1987-0869226-5
Keywords: Retraction, lifting, ultrafilter, $ c$-OK set, $ \beta {\mathbf{N}}$
Article copyright: © Copyright 1987 American Mathematical Society

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