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The machinery of braided geometry introduced previously is used now toconstruct the $\epsilon$ `totally antisymmetric tensor' on a general braidedvector space determined by R-matrices. This includes natural $q$-Euclidean and$q$-Minkowski spaces. The formalism is completely covariant under thecorresponding quantum group such as $\widetilde{SO_q(4)}$ or$\widetilde{SO_q(1,3)}$. The Hodge $*$ operator and differentials are alsoconstructed in this approach.Comment: 24 pages, substantative revision - decided to include material on  Hodge * operator previously omitted. Added a figur

q-epsilon tensor for quantum and braided spaces