Let T us be the usual topology on R and T_I 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, T1) by f(x) = 2x and g the mapping...

Topology

Extracted text: Let T us be the usual topology on R and T_I 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, T1) by f(x) = 2x and g the mapping from (R, T_1I) into (R, T_us) by g(x) = 3x. Then O gis a homneomorphism but f is not O fand g are both homeomorphisms f is a homeomorphism but g is not O None of the choices