theorem Th40: :: COUSIN:55

for r, s being Real
for jauge being Function of [.r,s.],].0,+infty.[
for S being Subset-Family of (Closed-Interval-TSpace (r,s)) st r <= s & S = { (].(x - (jauge . x)),(x + (jauge . x)).[ /\ [.r,s.]) where x is Element of [.r,s.] : verum } holds
S is open