What makes a space have large weight?
What makes a space have large weight?
I. Juhasz, L. Soukup, Z. Szentmiklossy:
What makes a space have large weight?
In section 2 of this paper we formulate several conditions (two of them
are necessary and sufficient) which imply that a space of small character
has large weight. In section 3 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,
and 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.