I know that there are locally compact Hausdorff spaces that aren't normal. Are there examples which are second countable?
2026-03-25 15:45:24.1774453524
Is every second countable locally compact Hausdorff space normal?
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This search in pi-Base shows one reason why such spaces must be normal: https://topology.pi-base.org/spaces?q=Second%20Countable%2BLocally%20Compact%2B%24T_2%24%2B~Normal
In short, Hausdorff locally compact spaces are completely regular, and second countable regular Hausdorff spaces spaces are metrizable, and therefore normal.