We construct in ZFC a cosmic space that, despite being the union of countably many metrizable subspaces, has covering dimension equal to 1 and inductive dimensions equal to 2.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm192-1-4,
author = {Michael G. Charalambous},
title = {Resolving a question of Arkhangel'ski\u\i 's},
journal = {Fundamenta Mathematicae},
volume = {189},
year = {2006},
pages = {67-76},
zbl = {1107.54027},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm192-1-4}
}
Michael G. Charalambous. Resolving a question of Arkhangel'skiĭ's. Fundamenta Mathematicae, Tome 189 (2006) pp. 67-76. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm192-1-4/