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A graph is called $n$-connected if it remains connected after removal $\le n$ vertices.

Question. What is the name of an analogous property of topological spaces: a space that remains connected after removal of $\le n$ points.

Unfortunately, the term $n$-connected space is already occupied for naming topological spaces whose homotopy groups $\pi_k(X)$ are trivial for all $k\le n$.

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    $\begingroup$ For graphs, you have slightly different notions of k-vertex-connected (often shortened to just k-connected) and k-edge-connected ones. Why not borrow unabbreviated vertex-connectedness? Graph-theoretic definition is what you want verbatim. $\endgroup$
    – Denis T
    Commented Aug 31, 2022 at 13:38
  • $\begingroup$ @DenisT Thanks for the suggestion, which I have used (i.e., vertex-connected). In fact I needed only 1-connected spaces, which became vertex-connected. $\endgroup$
    – Taras Banakh
    Commented Sep 1, 2022 at 13:20

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