István Juhász, Lajos Soukup and
Zoltán Szentmiklóssy

We introduce a ZFC method that enables us to build
spaces (in fact special dense subspaces of certain Cantor cubes)
in which we have "full control" over all dense
subsets.

Using this method we are able to construct, in ZFC,
for each uncountable regular cardinal
a 0-dimensional , hence Tychonov, space which is -resolvable
for all
but not
-resolvable. This yields the final (negative) solution of a
celebrated
problem of Ceder and Pearson raised in [3]: Are -resolvable
spaces maximally resolvable?

This method enables us to solve several other open problems as well, like
[1, Question 4.4], [2, Problem 8.6],
[5, Questions 3.4, 3.6, 4.5], and [4, Question 3.11].

Alas, O. T., Sanchis, M., Tkacenko, M. G., Tkachuk, V. V.; Wilson, R. G.
Irresolvable and submaximal spaces: homogeneity versus
-discreteness and new ZFC examples.
Topology Appl. 107 (2000), no. 3, 259-273.