This is a follow-up on an older question.
Let $\Box_{i\in I} X_i$ denote the box product of the spaces $X_i$. Is there a Hausdorff space $(X,\tau)$ with $|X|>1$ such that $\Box_{n\in\omega}X$ connected?
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Sign up to join this communityThis is a follow-up on an older question.
Let $\Box_{i\in I} X_i$ denote the box product of the spaces $X_i$. Is there a Hausdorff space $(X,\tau)$ with $|X|>1$ such that $\Box_{n\in\omega}X$ connected?
If $X$ is the Irrational slope topology then the closures of any two non-empty open sets must intersect. It easily follows that $\Box_{n\in\omega}X$ is connected. Note that $X$ is Hausdorff but not regular. It seems (see the comments to the OP) that there are no $T_3$ examples.