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, T_us) into (R, T_II) by f(x) =1 and g the mapping from (R, T_II) into (R, T_us) by g(x) = 4x. Then * None of the choices O f and g are both homeomorphisms f is a homeomorphism but g is not g is a homeomorphism but f is not

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