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/