Abstract| In this paper, some fundamental limitations of projective invariants of non-algebraic planar curves are discussed. It is shown that all curves within a large class can be mapped arbitrarily close to a circle by projective transformations. It is also shown that arbitrarily close to each of a nite number of closed planar curves there is one member of a set of projectively equivalent curves. Thus a continuous projective invariant on closed curves is constant. This also limits the

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... ity of nding so called projective normalisation schemes for closed planar curves. Keywords| Projective and a ne invariants, recognition, Hausdor metric.