theorem LMTh3: :: LOPBAN13:23

for X, Y being non trivial RealBanachSpace
for u being Point of (R_NormSpace_of_BoundedLinearOperators (X,Y)) st u is invertible holds
for r being Real st 0 < r holds
ex s being Real st
( 0 < s & ( for v being Point of (R_NormSpace_of_BoundedLinearOperators (X,Y)) st ||.(v - u).|| < s holds
||.((Inv v) - (Inv u)).|| < r ) )