docs.google.com Every infinite subset of X is dense in X Let T_us be the usual topology on R and T_IIl be the lower limit topology generated by the unions of {]a,b]/ a,bER;asb}. Define f the mapping...

Extracted text: docs.google.com Every infinite subset of X is dense in X Let T_us be the usual topology on R and T_IIl 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 %3D (R, T_us) by g(x) = 4x. Then * g is a homeomorphism but f is not f and g are both homeomorphisms f is a homeomorphism but g is not None of the choices Let f be a mapping from ]0,2[ to [1,+co[ defined by f(x) = 1/x. Then * %3D None of the choic >