Geodesic
Paracompactness for Ordered Sums
Canadian mathematical bulletin, Tome 21 (1978) no. 3, pp. 363-364

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Let us say that an order embedding of an uncountable regular cardinal in a linearly ordered set is continuous if it preserves the suprema (for all smaller limit ordinals). This makes the embedding a homeomorphism for the two order topologies; and if the image has no supremum, it is a closed subspace. Since uncountable regular cardinals fail to be paracompact, a linearly ordered set can be paracompact only if it admits no such embedding or anti-embedding. Conversely, Gillman and Henriksen have shown that this suffices (Trans. A.M.S. 77 (1954) pp. 352 ff). 
Fleischer, Isidore. Paracompactness for Ordered Sums. Canadian mathematical bulletin, Tome 21 (1978) no. 3, pp. 363-364. doi: 10.4153/CMB-1978-063-5
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     title = {Paracompactness for {Ordered} {Sums}},
     journal = {Canadian mathematical bulletin},
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     year = {1978},
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     doi = {10.4153/CMB-1978-063-5},
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