Geodesic
On the remainders of compactifications of mappings
Izvestiya. Mathematics , Tome 71 (2007) no. 3, pp. 441-448.

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We generalize Magill's theorems to locally compact Hausdorff mappings. We also give another description of all remainders of compactifications of a locally compact Hausdorff space and extend this description to locally compact Hausdorff and Tychonoff mappings. 
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E. N. Belyanova. On the remainders of compactifications of mappings. Izvestiya. Mathematics , Tome 71 (2007) no. 3, pp. 441-448. http://geodesic.mathdoc.fr/item/IM2_2007_71_3_a1/

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[4] E. N. Belyanova, “Opisanie vsekh $T_2$-bikompaktifikatsii lokalno bikompaktnogo $T_2$-prostranstva”, Nauch. tr. MPGU, Prometei, M., 2004, 13–19