{"date_updated":"2025-12-12T23:12:38Z","date_created":"2025-12-12T23:07:55Z","type":"preprint","status":"public","author":[{"last_name":"Khanfir","full_name":"Khanfir, Robin","first_name":"Robin"},{"first_name":"Beranger Fabrice","id":"102487","last_name":"Seguin","full_name":"Seguin, Beranger Fabrice"}],"language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"We study $n$-flimsy spaces, which are the topological spaces that remain connected when removing fewer than $n$ points but become disconnected when removing exactly $n$ points. We show that no such space exists for $n \\geq 3$, and that the compact $2$-flimsy spaces are precisely the dense and order-complete cyclically ordered sets equipped with their order topology. Furthermore, we examine variants of the definition obtained by replacing connectedness by path-connectedness, where paths are either parametrized by $[0,1]$ or by arbitrary compact linear continua."}],"external_id":{"arxiv":["2511.17745"]},"publication":"arXiv:2511.17745","user_id":"102487","_id":"63077","title":"Flimsy Spaces","citation":{"apa":"Khanfir, R., &#38; Seguin, B. F. (2025). Flimsy Spaces. In <i>arXiv:2511.17745</i>.","chicago":"Khanfir, Robin, and Beranger Fabrice Seguin. “Flimsy Spaces.” <i>ArXiv:2511.17745</i>, 2025.","short":"R. Khanfir, B.F. Seguin, ArXiv:2511.17745 (2025).","ama":"Khanfir R, Seguin BF. Flimsy Spaces. <i>arXiv:251117745</i>. Published online 2025.","bibtex":"@article{Khanfir_Seguin_2025, title={Flimsy Spaces}, journal={arXiv:2511.17745}, author={Khanfir, Robin and Seguin, Beranger Fabrice}, year={2025} }","mla":"Khanfir, Robin, and Beranger Fabrice Seguin. “Flimsy Spaces.” <i>ArXiv:2511.17745</i>, 2025.","ieee":"R. Khanfir and B. F. Seguin, “Flimsy Spaces,” <i>arXiv:2511.17745</i>. 2025."},"year":"2025"}