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, Tus) into (R, T_I) by f(x) = 2x and g the mapping...

Let T_us be the usual topology on R and T II be the lower limit topology<br>generated by the unions of (]a,b]/ a,beR;asb}. Define f the mapping from (R,<br>Tus) into (R, T_I) by f(x) = 2x and g the mapping from (R, T_II) into (R, T_us) by g(x)<br>%3D<br>= 3x. Then *<br>O fand g are both homeomorphisms<br>O fis a homeomorphism but g is not<br>O g is a homeomorphism but f is not<br>None of the choices<br>Which one of the following statements is true?<br>

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, Tus) into (R, T_I) by f(x) = 2x and g the mapping from (R, T_II) into (R, T_us) by g(x) %3D = 3x. Then * O fand g are both homeomorphisms O fis a homeomorphism but g is not O g is a homeomorphism but f is not None of the choices Which one of the following statements is true?

Jun 05, 2022

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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, Tus) into (R, T_I) by f(x) = 2x and g the mapping...

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