We prove that, for every finite-dimensional metrizable space, there exists a compactification that is Eberlein compact and preserves both the covering dimension and weight.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm171-3-3, author = {Takashi Kimura and Kazuhiko Morishita}, title = {On Eberlein compactifications of metrizable spaces}, journal = {Fundamenta Mathematicae}, volume = {173}, year = {2002}, pages = {223-234}, zbl = {1035.54015}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm171-3-3} }
Takashi Kimura; Kazuhiko Morishita. On Eberlein compactifications of metrizable spaces. Fundamenta Mathematicae, Tome 173 (2002) pp. 223-234. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm171-3-3/