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manuscripta mathematica

, Volume 22, Issue 1, pp 77–85 | Cite as

Uncountable powers of\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{R}\) can be almost Lindelöf

  • D. H. Fremlin
Article

Abstract

Moran ([6]) and, independently, Kemperman & Maharam ([4]) have shown that\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{R} ^\mathbb{C}\) is not almost Lindelöf. Hechler ([3]) showed that\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{R} ^{\aleph _1 }\) may fail to be almost Lindelöf whether or not the continuum hypothesis is true. In this paper I shall prove that, if Martin's Axiom is assumed, then\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{R} ^K\) is almost Lindelöf for every k<ℂ; so that, in particular, it is possible for\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{R} ^{\aleph _1 }\) to be almost Lindelöf. The novel part of the argument is contained in Theorem 7, which does not depend on Martin's Axiom.

Keywords

Number Theory Algebraic Geometry Topological Group Continuum Hypothesis Uncountable Power 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Springer-Verlag 1977

Authors and Affiliations

  • D. H. Fremlin
    • 1
  1. 1.Department of MathematicsUniversity of EssexColchesterEngland

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