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arXiv · 2511.17745

Flimsy Spaces

Robin Khanfir·Béranger Seguin
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Abstract

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.

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Robin Khanfir, Béranger Seguin. 2025-11-21. Flimsy Spaces. https://arxiv.org/abs/2511.17745

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