Geodesic
Note on "Paracompactness in Small Products"
Canadian mathematical bulletin, Tome 16 (1973) no. 4, pp. 595-596

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In [1], Willard proves the following If a regular paracompact space X has a dense Lindelöfsubspace, then X is Lindelöf.Willard notes that the above is a generalization of the standard theorem: A separable paracompact space is Lindelöf. Actually, it is a standard fact ([2, p. 24]) that a separable metacompact space is Lindelöf. Moreover, one discovers that if a separable space X is such that each open cover of X has a point-countable open refinement, then X is Lindelöf. 
Chew, James. Note on "Paracompactness in Small Products". Canadian mathematical bulletin, Tome 16 (1973) no. 4, pp. 595-596. doi: 10.4153/CMB-1973-097-6
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     title = {Note on {"Paracompactness} in {Small} {Products"}},
     journal = {Canadian mathematical bulletin},
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     year = {1973},
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     number = {4},
     doi = {10.4153/CMB-1973-097-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1973-097-6/}
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