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First Countable Continua and Proper Forcing

Published:2009-06-01
Printed: Jun 2009
• Joan E. Hart
• Kenneth Kunen
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Abstract

Assuming the Continuum Hypothesis, there is a compact, first countable, connected space of weight $\aleph_1$ with no totally disconnected perfect subsets. Each such space, however, may be destroyed by some proper forcing order which does not add reals.
 Keywords: connected space, Continuum Hypothesis, proper forcing, irreducible map
 MSC Classifications: 54D05 - Connected and locally connected spaces (general aspects) 03E35 - Consistency and independence results