The Fine Topology

Let (x _n ) be a sequence of points in B\{0} converging to 0, and let 7.1.1% MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % qacaWG1bWaaeWaa8aabaWdbiaadIhaaiaawIcacaGLPaaacqGH9aqp % daaeWbWdaeaapeGaaGOma8aadaahaaWcbeqaa8qacqGHsislcaWGUb % aaaOGaamyva8aadaWgaaWcbaWdbiaadIhapaWaaSbaaWqaa8qacaWG % UbaapaqabaaaleqaaOWdbmaabmaapaqaa8qacaWG4baacaGLOaGaay % zkaaGaai4laiaadMfapaWaaSbaaSqaa8qacaWG4bWdamaaBaaameaa % peGaamOBaaWdaeqaaaWcbeaak8qadaqadaWdaeaapeGaaGimaaGaay % jkaiaawMcaaaWcpaqaa8qacaWGUbGaeyypa0JaaGymaaWdaeaapeGa % eyOhIukaniabggHiLdGcpaGaaGzbV-qadaqadaWdaeaapeGaamiEai % abgIGiolaadkfapaWaaWbaaSqabeaapeGaamOtaaaaaOGaayjkaiaa % wMcaaiaac6caaaa!59E9!$$ u\left( x \right) = \sum\limits_{n = 1}^\infty {{2^{ - n}}{U_{{x_n}}}\left( x \right)/{Y_{{x_n}}}\left( 0 \right)} \quad \left( {x \in {R^N}} \right).$$