Locally countably-compact Hausdorff groups act continuously on their Milnor joins and cones, with equivalent characterizations extending the local compactness-exponentiability link.
Cambridge: Cambridge University Press, 2002
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Discontinuous actions on cones, joins, and $n$-universal bundles
Locally countably-compact Hausdorff groups act continuously on their Milnor joins and cones, with equivalent characterizations extending the local compactness-exponentiability link.