Editing problem correction: "F" in the first sentence should read "S". Sorry about that. (Also note that s_1 = s_2 is not excluded.) --Dan << The "shrine problem" is, given a family S of shapes (let's say certain subsets of R^n) for which it makes sense to talk about a continuous curve [0,1] -> F, find a selection function P: S -> R^n such that for all s in S, P(s) is a member of s. P must also satisfy two conditions: 1) Given a continuous curve of shapes s:[0,1] -> S, the map [0,1] -> R^n given by t |-> P(s_t) is continuous, and 2) If some isometry I: R^n -> R^n carries one shape s_1 of S onto another one s_2, then P(s_2) = I(P(s_1)).
________________________________________________________________________________________ It goes without saying that .