Given global semianalytic sets A and B, we define a minimal analytic set N such that Ā∖N and B̅∖N can be separated by an analytic function. Our statement is very similar to the one proved by Bröcker for semialgebraic sets.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap95-2-8, author = {Hamedou Diakite}, title = {Separation of global semianalytic sets}, journal = {Annales Polonici Mathematici}, volume = {95}, year = {2009}, pages = {179-186}, zbl = {1165.14038}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap95-2-8} }
Hamedou Diakite. Separation of global semianalytic sets. Annales Polonici Mathematici, Tome 95 (2009) pp. 179-186. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap95-2-8/