Let T_us be the usual topology on R and T_II be the lower limit topology generated by the unions of {]a,b]/ a,bER;asb}. Define f the mapping from (R, T_us) into (R, T_II) by f(x) = 2x and g the...

Extracted text: Let T_us be the usual topology on R and T_II be the lower limit topology generated by the unions of {]a,b]/ a,bER;asb}. Define f the mapping from (R, T_us) into (R, T_II) by f(x) = 2x and g the mapping from (R, T_II) into (R, T_us) by g(x) = 3x. Then * %3D g is a homeomorphism but f is not f is a homeomorphism but g is not None of the choices O f and g are both homeomorphisms