Expansive homeomorphisms on quasi-metric spaces





Expansive homeomorphism, canonical coordinates, hyperbolic coordinates


The investigation of expansive homeomorphisms in metric spaces began with Utz in 1950. Thereafter, several authors have extensively studied this concept for different motivations. In this current article, we study expansive homeomorphism in the context of quasi-pseudometric spaces. This is motivated by the fact that any expansive homeomorphism on quasi-pseudometric space is again expansive homeomorphism on its induced pseudometric space but the converse is not true in general. Moreover, the study of orbit structures has been taken to consideration in this article. For instance, we investigate the denseness of orbits in the context of quasi-metric spaces.


Download data is not yet available.


N. Aoki, Topological dynamics. Topics in general topology, 625-740, North-Holland Math. Library, 41, North-Holland, Amsterdam, 1989. https://doi.org/10.1016/S0924-6509(08)70161-2

A. Arbieto and C. A. Morales, Expansive measures, Pulb. Mat. Urug. 14 (2013), 61-71.

R. Bowen, Topological entropy and Axiom A, Proc. Sympos. in: Pure Math. Amer. Math. Soc. XIV (1970), 23-41. https://doi.org/10.1090/pspum/014/9986

R. Bowen, Equilibrium states and the ergodic theory of Anosov diffeomorphisms, Lecture Notes in Math. 470. Springer, Berlin, 1970.

M. de Brecht, Quasi-Polish spaces, Ann. Pure Appl. Logic. 164 (2013), 356-381. https://doi.org/10.1016/j.apal.2012.11.001

B. F. Bryant, Expansive self-homeomorphisms of a compact metric Space, Amer. Math. Monthly. 69 (1962), 386-391. https://doi.org/10.1080/00029890.1962.11989902

S. Cobzas, Functional Analysis in Asymmetric Normed Spaces, Frontiers in Mathematics, Springer, Basel, 2012. https://doi.org/10.1007/978-3-0348-0478-3

P. Fletcher and W. F. Lindgren, Quasi-Uniform Spaces, vol. 77 of Lecture Notes in Pure and Applied Mathematics, Marcel Dekker, New York, NY, USA, 1982.

J. Goubault-Larrecq, Non-Hausdorff topology and domain theory-selected topics in point-set topology, New Mathematical Monographs. 22. Cambridge University Press, Cambridge, 2013. https://doi.org/10.1017/CBO9781139524438

H. P. Künzi and F. Yildiz, Convexity structures in $T_0$-quasi-metric spaces, Topology Appl. 200 (2016), 2-18. https://doi.org/10.1016/j.topol.2015.12.009

C. A. Morales and V. F. Sirvent, Expansive measures. Publicaçoes Matemáticas do IMPA. [IMPA Mathematical Publications] 29º Colóquio Brasileiro de Matemática. [29th Brazilian Mathematics Colloquium] Instituto Nacional de Matemática Pura e Aplicada (IMPA), Rio de Janeiro, 2013. viii+89 pp.

C. A. Morales and V. Sirvent, Expansivity for measures on uniform spaces, Trans. Amer. Math. Soc. 368 (2016), 5399-5414. https://doi.org/10.1090/tran/6555

W. L. Reddy, Expansive canonical coordinates are hyperbolic, Topology Appl. 15 (1983), 205-210. https://doi.org/10.1016/0166-8641(83)90038-X

A. Stojmirovic, Quasi-metric spaces with measures, Topology Proc. 28 (2004), 655-671.

W. R. Utz, Unstable homeomorphism, Proc. Amer. Math. Soc. 1 (1950), 769-774. https://doi.org/10.1090/S0002-9939-1950-0038022-3

A. W. Wilson, On quasi-metric spaces, Amer. J. Math. 53 (1931), 675-684. https://doi.org/10.2307/2371174




How to Cite

O. Olela Otafudu, D. P. Matladi, and M. S. Zweni, “Expansive homeomorphisms on quasi-metric spaces”, Appl. Gen. Topol., vol. 25, no. 1, pp. 1–15, Apr. 2024.



Regular Articles