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There is a result that if two manifolds ## M_1, M_2 ## ( I don't know to what extent this generalizes to other topological spaces) intersect transversally, say in ##\mathbb R^m ## , then the dimension of the intersecting set is given by m - ##\Sigma Cod(M_i ) ; i=1,2##, where ##Cod(M_i):= m-Dim(M_i)##, i.e., the dimension of the ambient space minus the dimension of the manifold. Is there any result for intersections of 3- or more manifolds, i.e., for the case where the intersecting set contains points of all 3 manifolds? Do we consider pairwise transversal intersection, etc.?

Thanks,

WWGD: What Would Gauss Do?

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# Transversal Intersection of More than 2 Surfaces

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