We know that a subspace of a connected space can be disconnected eg. $\mathbf{Q} \in \mathbf{R}$ where $\mathbf{R}$ is connected but $\mathbf{Q}$ is totally disconnected as a subspace. My question is, "Does there exists a topological space such that every proper subspace (except singletons) is disconnected but the whole space is connected".
2026-03-30 16:21:44.1774887704
Connected space whose every subspace is disconnected
1.3k Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in GENERAL-TOPOLOGY
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