Let T_us be the usual topology on R and T Il be the lower limit topology generated by the unions of {Ja,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 Il be the lower limit topology generated by the unions of {Ja,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 O f and g are both homeomorphisms None of the choices g is a homeomorphism but f is not f is a homeomorphism but g is not