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First Countable Continua and Proper Forcing

Published online by Cambridge University Press:  20 November 2018

Joan E. Hart  and
Kenneth Kunen
Joan E. Hart
Affiliation:
University ofWisconsin, Oshkosh, WI 54901, USA, [email protected]
Kenneth Kunen
Affiliation:
University ofWisconsin, Madison, WI 53706, USA, [email protected]
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Abstract

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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

54D0503E35connected spaceContinuum Hypothesisproper forcingirreducible map
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 61 , Issue 3 , 01 June 2009 , pp. 604 - 616
Copyright
Copyright © Canadian Mathematical Society 2009

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