A Characterization of Self-similar Symbolic Spaces

F.G. Arenas, M.A. Sánchez-Granero, A characterization of non-archimedeanly quasimetrizable spaces, Rend. Istit. Mat. Univ. Trieste, Suppl. Vol. XXX (1999), 21–30.

Arenas F.G., Sánchez-Granero M.A.: A new approach to metrization. Topology Appl. 123(1), 15–26 (2002)

F.G. Arenas, M.A. Sánchez-Granero, A new metrization theorem, Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8), 5-B (2002), 109–122.

Arenas F.G., Sánchez-Granero M.A.: Hahn-Mazurkiewicz revisited: a new proof. Houston J. Math. 28(4), 753–769 (2002)

Arenas F.G., Sánchez-Granero M.A.: Completeness in metric spaces. Indian J. Pure Appl. Math. 33(8), 1197–1208 (2002)

Arenas F.G., Sánchez-Granero M.A.: Completeness in GF-spaces. Far East J. Math. Sci. (FJMS) 10(3), 331–351 (2003)

F.G. Arenas, M.A. Sánchez-Granero, Dimension, inverse limits and GF-spaces, Rend. Istit. Mat. Univ. Trieste XXXV (2003), 19–35.

Bandt C., Keller K.: Self-similar sets 2: a simple approach to the topological structure of fractals. Math. Nachr. 154, 27–39 (1991)

C. Bandt and T. Retta, Self-similar sets as inverse limits of finite topological spaces, Topology, measures, and fractals (Warnemunde, 1991), 41–46. Akademie-Verlag, Berlin, 1992.

Bandt C., Retta T.: Topological spaces admitting a unique fractal structure. Fund. Math. 141, 257–268 (1992)

Bandt C., Hung N.V., Rao H.: On the open set condition for self-similar fractals. Proc. Amer. Math. Soc. 134(5), 1369–1374 (2006)

Bandt C., Hung N.V.: Self-similar sets with an open set condition and great variety of overlaps. Proc. Amer. Math. Soc. 136(11), 3895–3903 (2008)

Charatonik W.J., Dilks A.: On self-homeomorphic spaces. Topology Appl. 55, 215–238 (1994)

K. Falconer, Fractal geometry, Mathematical Foundations and Applications, John Wiley & Sons, 1990.

Feder J.: Fractals. Plenum Press, New York (1988)

P. Fletcher and W.F. Lindgren, Quasi-uniform spaces, Lecture Notes Pure Appl. Math. 77, Marcel Dekker, New York, 1982.

G. Gruenhage, Generalized metric spaces, chapter 10 of K.Kunen, J.E. Vaughan (ed.), Handbook of set-theoretic topology, Elsevier Science Publishers B.V., 1984.

M. Hata, Fractals-On self-similar sets. Sugaku Expositions 6-1, 1993.

Hata M.: On some properties of set-dynamical systems. Proc. Japan Acad. Ser. A Math. Sci. 61, 99–102 (1985)

Hata M.: On the structure of self-similar sets. Japan J. Indust. Appl. Math. 2, 381–414 (1985)

M. Hata, Topological aspects of self-similar sets and singular functions, Fractal Geometry and Analysis, 255–276. Kluwer Academic Publishers, Dordrecht, 1991.

B. Mandelbrot, R.L. Hudson, The (mis) behavior of markets. Basic Books, 2004.

Hutchison J.E.: Fractal and self-similarity. Indiana Univ. Math. J. 30, 713–747 (1981)

Kameyama A.: Self-similar sets from the topological point of view. Japan J. Indust. Appl. Math. 10, 85–95 (1993)

Romaguera S., Shore S.D.: Metrizability of asymmetric spaces. Ann. New. York Acad. Sci. 806, 382–392 (1996)

S. Willard, General topology, Addison-Wesley, 1970.