Abstract

In mathematical approach to the pattern recognition there are some mathematical problems that are important for practical aims. One of them is invariance of geometrical shape with respect to the Hausdorff convergence. In this paper we prove that the limit of a convergent sequence of compact sets in $R^n$ of the same shape is again a set of the same shape or a singleton.

Keywords: Geometric shape, Hausdorff metric, general position.

MSC: 68T10, 54B20

Pages:  25$-$28     

Volume  48 ,  Issue  1$-$2 ,  1996