Let (T: X ightarrow Y) be any map. Show that (T^{-1}(sigma(mathscr{G}))=sigmaleft(T^{-1}(mathscr{G})ight)) holds for arbitrary families (mathscr{G}) of
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Let \(T: X ightarrow Y\) be any map. Show that \(T^{-1}(\sigma(\mathscr{G}))=\sigma\left(T^{-1}(\mathscr{G})ight)\) holds for arbitrary families \(\mathscr{G}\) of subsets of \(Y\).
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We have T G CT G oTG CT 6G is itself a oalgebra For the converse consider T X GTG YoG By the v...View the full answer
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