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Comparison of Lasso and Whisker topologies on fundamental groupoids and local triviality | ||
| Journal of Mahani Mathematical Research | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 28 مرداد 1404 اصل مقاله (446.08 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmr.2025.24987.1776 | ||
| نویسنده | ||
| Ali Pakdaman* | ||
| Department of Mathematics, Faculty of Sciences, Golestan University, Gorgan, Iran | ||
| چکیده | ||
| This paper is devoted to comparing the Lasso topology and the Whisker topology on the fundamental groupoid. We prove that for locally path connected and semilocally simply connected spaces, the two topologies coincide. However, the converse does not hold in general, and we provide a partial converse. Furthermore, we observe that the topological fundamental groupoid is not étale, and we show that the topological fundamental groupoids of locally path connected and semilocally simply connected spaces, equipped with these topologies, are locally trivial. Through several examples, we illustrate the necessity of these conditions | ||
| کلیدواژه‌ها | ||
| Topological fundamental groupoid؛ Locally trivial groupoid؛ Lasso topology؛ Whisker topology | ||
| مراجع | ||
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[13] Pakdaman, A., & Shahini, F. (2023). Fundamental groupoid and whisker topology, Mathematical researches, 9, 55{71.
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[15] Pashaei, S. Z., Mashayekhy, B., Torabi, H., & Abdullahi Rashid, M. (2019). On strong small loop transfer spaces relative to subgroups of fundamental groups, Topology and its applications, 254, 117{131. https://doi.org/10.1016/j.topol.2018.12.006
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آمار تعداد مشاهده مقاله: 6 تعداد دریافت فایل اصل مقاله: 6 |
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