We introduce the notion of a nonarchimedean size function similar to the notion of a size function introduced by Marcos. We describe a class of ring topologies on fields that are complete, neither first countable nor locally bounded, but have topologically nilpotent elements.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm183-2-2, author = {Niel Shell}, title = {Size functions}, journal = {Fundamenta Mathematicae}, volume = {184}, year = {2004}, pages = {109-113}, zbl = {1076.54028}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm183-2-2} }
Niel Shell. Size functions. Fundamenta Mathematicae, Tome 184 (2004) pp. 109-113. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm183-2-2/