Let T us be the usual topology on R and T_Il be the lower limit topology generated by the unions of {]a,b]/ a,beR;asb}. Define f the mapping from (R, Tus) into (R, T_I) by f(x) = 2x and g the mapping from (R, T_II) into (R, T_us) by %3D g(x) = 3x. Then O gis a homeomorphism but f is not O fis a homeomorphism but g is not O fand g are both homeomorphisms O None of the choices

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