Geodesic
A generalization of Magill's Theorem for non-locally compact spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) no. 1, pp. 127-136.

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In the theory of compactifications, Magill's theorem that the continuous image of a remainder of a space is again a remainder is one of the most important theorems in the field. It is somewhat unfortunate that the theorem holds only in locally compact spaces. In fact, if all continuous images of a remainder are again remainders, then the space must be locally compact. This paper is a modification of Magill's result to more general spaces. This of course requires restrictions on the nature of the function.
Classification : 54D30, 54D35, 54D40
Keywords: compactifications; remainders 
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Faulkner, Gary D.; Vipera, M. Cristina. A generalization of Magill's Theorem for non-locally compact spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) no. 1, pp. 127-136. http://geodesic.mathdoc.fr/item/CMUC_1995__36_1_a15/