fis neither continuous nor a homeomorphism f is not continuous Let T us be the usual topology on R and T |l be the lower limit topology generated by the unions of (]a,b]/ a,beR;asb}. Define f the...

Extracted text: fis neither continuous nor a homeomorphism f is not continuous Let T us be the usual topology on R and T |l 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 1) by f(x)=1 and g the mapping from (R, TII) into (R, T_us) by g(x) = 4x. Then g is a homeomorphism but f is not None of the choices f and g are both homeomorphisms f is a homeomorphism but g is not Let X = (a, b, C, d.e) and let T = (X. o. (a). (a.d). (a.e)}, then (X T) is not Hausdorff but it is connected OXT) is not connected but it is Hausdorff (X T)is neither Hausdorff nor connected o search