reserve PM for MetrStruct;
reserve x,y for Element of PM;
reserve r,p,q,s,t for Real;
reserve T for TopSpace;
reserve A for Subset of T;
reserve T for non empty TopSpace;
reserve x for Point of T;
reserve Z,X,V,W,Y,Q for Subset of T;
reserve FX for Subset-Family of T;
reserve a for set;
reserve x,y for Point of T;
reserve A,B for Subset of T;
reserve FX,GX for Subset-Family of T;
reserve x,y,z for Element of PM;
reserve V,W,Y for Subset of PM;

theorem Th29:
  for r being Real st PM is triangle holds Ball(x,r) in
  Family_open_set(PM)
proof
  let r be Real;
  assume PM is triangle;
  then
  for y st y in Ball(x,r) holds ex p st p>0 & Ball(y,p) c= Ball(x,r) by Th27;
  hence thesis by Def4;
end;
