From Problems 2.9 and 2.11, the group D 2 = {e, a, b, c} has a factor

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From Problems 2.9 and 2.11, the group D2= {e, a, b, c} has a factor (quotient) group with respect to the abelian invariant subgroup \(H=\{e, a\}\),

\[\mathrm{D}_{2} / H=H+M=\{e, a\}+\{b, c\}\]

with a map \(\phi\) from \(\mathrm{D}_{2}\) to \(\mathrm{D}_{2} / H\) given by

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Show that if the space for \(\mathrm{D}_{2}\) is equipped with a topology defined by the open setsimage text in transcribedthe inverse map \(\phi^{-1}\) implies that the quotient space has a topology also.

Data from Problem 2.9

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Data from Problem 2.11

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