We prove that the infimum of the regular separation exponents of two subanalytic sets at a point is a rational number, and it is also a regular separation exponent of these sets. Moreover, we consider the problem of attainment of this exponent on analytic curves.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap87-0-21, author = {Stanis\l aw Spodzieja}, title = {The \L ojasiewicz exponent of subanalytic sets}, journal = {Annales Polonici Mathematici}, volume = {85}, year = {2005}, pages = {247-263}, zbl = {1095.32004}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap87-0-21} }
Stanisław Spodzieja. The Łojasiewicz exponent of subanalytic sets. Annales Polonici Mathematici, Tome 85 (2005) pp. 247-263. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap87-0-21/