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If you want a closed discrete set take the metric hedgehog with $\kappa$ many spines, where $\kappa$ is the desired cardinality. If $\kappa<\mathfrak{c}$ replace $[0,1]$ by a countable connected Hausdorff space, as in Will Brian's answer.
If you want a closed discrete set take the metric hedgehog with $\kappa$ many spines, where $\kappa$ is the desired cardinality.
If you want a closed discrete set take the metric hedgehog with $\kappa$ many spines, where $\kappa$ is the desired cardinality. If $\kappa<\mathfrak{c}$ replace $[0,1]$ by a countable connected Hausdorff space, as in Will Brian's answer.
