Suppose I have $B=F^{-1}(A)$, shouldn’t $F^{-1}$ defined on all of $A$ for the inverse map to make sense? Or can we define $B=({{ u\in B|F(u)\in A }})$? My question is regarding a proof in Pressley’s Elementary Differential Geometry. How is $\tilde{\sigma}^{-1}$ defined on all of $\sigma(W)$?
can someone explain this?
2026-03-25 17:37:10.1774460230
Inverse Map of a Set
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