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The induced contractive maps on the covering spaces | ||
Caspian Journal of Mathematical Sciences | ||
مقاله 10، دوره 10، شماره 1، مهر 2021، صفحه 85-92 اصل مقاله (90.2 K) | ||
نوع مقاله: Research Articles | ||
شناسه دیجیتال (DOI): 10.22080/cjms.2020.18710.1487 | ||
نویسندگان | ||
Zahra Shabani Siahkalde* 1؛ Tayyebe Nasri2 | ||
1Department of Mathematics, Faculty of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran | ||
2Department of Pure Mathematics, Faculty of Basic Sciences, University of Bojnord, Bojnord, Iran | ||
تاریخ دریافت: 22 اردیبهشت 1399، تاریخ بازنگری: 27 مرداد 1399، تاریخ پذیرش: 30 مرداد 1399 | ||
چکیده | ||
Let $(\tilde{X},p)$ be the universal covering space of a compact metrizable space $ X $, which is compact and locally path connected. In this paper, we show that there exist metrics $ d $ and $ d' $ for $ X $ and $\tilde{X} $, respectively, such that any contractive map $ f:X\to X $ induces a contractive map on $ \tilde{X}$. As an application, it is obtained that every iterated function system(IFS) on the space $ X $ with attractor $ K $, induces an IFS on $\tilde{ X} $ with attractor $\tilde{K},$ such that $ p(\tilde{K})=K$. | ||
کلیدواژهها | ||
Covering spaces؛ Iterated function systems؛ Contractive maps | ||
آمار تعداد مشاهده مقاله: 179 تعداد دریافت فایل اصل مقاله: 231 |