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Compact Sets without Converging Sequences in the Random Real Model

Author(s): A. Dow | D. Fremlin

Journal: Acta Mathematica Universitatis Comenianae
ISSN 0862-9544

Volume: LXXVI;
Issue: 2;
Start page: 161;
Date: 2007;
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Keywords: random reals | converging sequences | Efimov problem

It is shown that in the model obtained by adding any number of random reals to a model of CH, there is a compact Hausdorff space of weight w1 which contains no non-trivial converging sequences. It is shown that for certain spaces with noconverging sequences, the addition of random reals will not add any converging sequences.
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