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In the present paper we construct Virtual Element Spaces that are $H({\rmdiv})$-conforming and $H({\rm \bf curl})$-conforming on general polygonal andpolyhedral elements; these spaces can be interpreted as a generalization ofwell known Finite Elements. We moreover present the basic tools needed to makeuse of these spaces in the approximation of partial differential equations.Finally, we discuss the construction of exact sequences of VEM spaces.

H(div) and H(curl)-conforming VEM