let F be Function of T,R^1; :: thesis: ( F = f " implies F is continuous )
assume A1: F = f " ; :: thesis: F is continuous
dom f = the carrier of T by FUNCT_2:def 1;
then for q being Point of T holds f . q <> 0 ;
then consider g being Function of T,R^1 such that
A2: for p being Point of T
for r being Real st f . p = r holds
g . p = 1 / r and
A3: g is continuous by JGRAPH_2:26;
F = g

proof

let x be Point of T; :: according to FUNCT_2:def 8 :: thesis: F . x = g . x
thus F . x = 1 / (f . x) by A1, VALUED_1:10
.= g . x by A2 ; :: thesis: verum

end;

hence F is continuous by A3; :: thesis: verum