Let A and C be subset of with boundaries B(A), B(C) respectively. Prove or disprove:
(1) B(AUC) = B(A)UB(C)
(2) B(A C) = B(A) B(C)
I haven't studied this formally per se, but both (1) and (2) seem to fail when we consider the simple case of two intersecting spheres in R^3, or even just intersecting discs in R^2.
Edit: Actually easier to write in ,
let ,
so
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Last edited by undefined; September 14th 2010 at 10:13 PM.
I haven't studied this formally per se, but both (1) and (2) seem to fail when we consider the simple case of two intersecting spheres in R^3, or even just intersecting discs in R^2.