Abstract
We show that intrinsic isometry does not have to preserve a fractal dimension.
Similar content being viewed by others
References
Alexandrov, V.: An example of a one-dimensional rigid set in the plane,Siberian Math. J. 34 (6) (1993), 3–9 (in Russian).
Borsuk, K.: On intrinsic isometries,Bull. Acad. Pol. Sci. 29 (1981), 83–90.
Cobb, J.: Two examples concerning small intrinsic isometries,Fund. Math. 131 (1988), 209–213.
Falconer, K. J.:Fractal Geometry, Wiley, New York, 1990.
Herburt, I.: On intrinsic isometries and rigid subsets of Euclidean spaces,Dem. Math. 22 (1989), 1205–1227.
Herburt, I.: Rigidity of products,Geom. Dedicata 46 (1993), 241–248.
Herburt, I.: Some (n − 1)-dimensional rigid sets inR n,Geom. Dedicata 49 (1994), 221–230.
Herburt, I. and Moszyńska, M.: On intrinsic embeddings,Glasnik Mat. 22 (42) (1987), 421–427.
Herburt, I. and Moszyńska, M.: On metric products,Coll. Math. 62 (1991), 121–133.
Herburt, I., Moszyńska, M. and Rudnik, K.: Spaces with intrinsically invariant fractal dimensions,Glasnik Mat. (to appear).
Moszyńska, M.: On rigid subsets of some manifolds,Coll. Math. 57 (1989), 247–254.
Olędzki, J. and Spież, S.: Remarks on intrinsic isometries,Fund. Math. 119 (1983), 241–247.
Rudnik, K.: Concerning the rigidity problem for subsets ofE 2,Bull. Acad. Pol. Sci. 37 (1989), 251–254.