The theorem in the title is proven. Applications to product theorems are given.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba54-2-6, author = {Iwo Labuda}, title = {Alexander Subbase Theorem for Filters}, journal = {Bulletin of the Polish Academy of Sciences. Mathematics}, volume = {54}, year = {2006}, pages = {147-152}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba54-2-6} }
Iwo Labuda. Alexander Subbase Theorem for Filters. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 54 (2006) pp. 147-152. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba54-2-6/