reserve a for Real;
reserve p,q for Point of TOP-REAL 2;

theorem Th96:
  for sn being Real, B0 being Subset of TOP-REAL 2,K0 being
Subset of (TOP-REAL 2)|B0,f being Function of ((TOP-REAL 2)|B0)|K0,((TOP-REAL 2
)|B0) st -1<sn & sn<1 & f=(sn-FanMorphE)|K0 & B0=NonZero TOP-REAL 2 & K0={p: p
  `1<=0 & p<>0.TOP-REAL 2} holds f is continuous
proof
  let sn be Real, B0 be Subset of TOP-REAL 2,
K0 be Subset of (TOP-REAL 2)|B0,f
  be Function of ((TOP-REAL 2)|B0)|K0,((TOP-REAL 2)|B0);
  the carrier of (TOP-REAL 2)|B0= B0 by PRE_TOPC:8;
  then reconsider K1=K0 as Subset of TOP-REAL 2 by XBOOLE_1:1;
  assume
A1: -1<sn & sn<1 & f=(sn-FanMorphE)|K0 & B0=NonZero TOP-REAL 2 & K0={p:
  p`1<=0 & p<>0.TOP-REAL 2};
  K0 c= B0
  proof
    let x be object;
    assume x in K0;
    then
A2: ex p8 being Point of TOP-REAL 2 st x=p8 & p8`1<=0 & p8 <>0.TOP-REAL 2
    by A1;
    then not x in {0.TOP-REAL 2} by TARSKI:def 1;
    hence thesis by A1,A2,XBOOLE_0:def 5;
  end;
  then ((TOP-REAL 2)|B0)|K0=(TOP-REAL 2)|K1 by PRE_TOPC:7;
  hence thesis by A1,Th94;
end;
