Let T us be the usual topology on R and Tl be the lower limit topology generated by the unions of (Ja,b]/ a,bcRasb}. Define f the mapping from (R, T us) into (R, TI) by f(x) - 1 and g the mapping from...

Extracted text: Let T us be the usual topology on R and Tl be the lower limit topology generated by the unions of (Ja,b]/ a,bcRasb}. Define f the mapping from (R, T us) into (R, TI) by f(x) - 1 and g the mapping from (R. T ) Into (R, T_us) by g(x) = 4x. Then* O gis a homeomorphism butf is not O fis a homeomorphism but g is not f and g are both homeomorphisms Oone of the choices