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finally, for completeness, there is also locally compact and second-countable spaces are sigma-compact
Am I right that the assumption of Hausdorff-ness serves the only purpose to avoid dealing with different notions of local compactness in case of non-Hausdorff spaces? If so, I would like to add a small comment on the role of the Hausdorff-ness assumption.
Thatâ€™s right. I fact I meant not to include the Hausdorff condition, but it seems then I did after all.
I have removed it now and added a remark after the locally compact clause.
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