Let T_us be the usual topology on R and T_II 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...

Topology


Extracted text: Let T_us be the usual topology on R and T_II 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 None of the choices f is a homeomorphism but g is not O g is a homeomorphism but f is not O f and g are both homeomorphisms