First Countable Continua and Proper Forcing
Printed: Jun 2009
Joan E. Hart
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.
connected space, Continuum Hypothesis, proper forcing, irreducible map
54D05 - Connected and locally connected spaces (general aspects)
03E35 - Consistency and independence results