I. Juhász, L. Soukup, Z. Szentmiklóssy:
What makes a space have large weight?
We formulate several conditions
(two of them are necessary and sufficient) which imply that a space
of small character has large weight.
- We construct a ZFC example of a 0-dimensional space
X of size 2^omega with w(X)=2^omega and chi(X)=nw(X)=omega,
- we show that CH implies the existence of a 0-dimensional space Y
of size omega_1 with w(Y)=nw(Y)=omega_1 and chi(Y)=R(Y)=omega,
- we prove that it is consistent that 2^omega is as large as you wish
and there is a 0-dimensional space Z of size 2^omega such that
w(Z)=nw(Z)=2^omega but chi(Z)=R(Z^omega)=omega.
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Topology and its Applications 57 (1994), no 2-3, 271--285.