In addition to being continuous, the canonical projections formula_54 are open maps. This means that any open subset of the product space remains open when projected down to the formula_29 The converse is not true: if formula_56 is a subspace of the product space whose projections down to all the formula_3 are open, then formula_56 need not be open in formula_7 (consider for instance formula_60) The canonical projections are not generally closed maps (consider for example the closed set formula_61 whose projections onto both axes are formula_62).