categories: Open maps of locales

[Walter Tholen <tholen@mathstat.yorku.ca>]

I need help with respect to the following question.
With the help of M.M. Clementino and J. Picado, I understood that an open
morphism f: X --> Y in the category of locales (dual to the category of
frames) has the property that taking inverse images (pullbacks) along
f commutes with taking closures of sublocales:  f*[cl(N)] = cl(f*[N]) for
all sublocales N of Y.
Conversely, does this property force f to be open (as it does for
topological spaces)? If not, is the answer positive when f is the
embedding of a sublocale?

I appreciate any suggestions/answers that you may have. Thanks,

Walter Tholen.