We provide examples of nonseparable compact spaces with the property that any continuous image which is homeomorphic to a finite product of spaces has a maximal prescribed number of nonseparable factors.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm202-1-4, author = {Antonio Avil\'es}, title = {Compact spaces that do not map onto finite products}, journal = {Fundamenta Mathematicae}, volume = {205}, year = {2009}, pages = {81-96}, zbl = {1166.54004}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm202-1-4} }
Antonio Avilés. Compact spaces that do not map onto finite products. Fundamenta Mathematicae, Tome 205 (2009) pp. 81-96. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm202-1-4/