Geodesic
Essential Extensions of T1-Spaces
Canadian mathematical bulletin, Tome 24 (1981) no. 2, pp. 237-240

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DOI

In the category of T1 -spaces and continuous maps, every space X has a unique maximal essential extension. X has an injective hull iff card X≤1. 
Hoffmann, Rudolf-E. Essential Extensions of T1-Spaces. Canadian mathematical bulletin, Tome 24 (1981) no. 2, pp. 237-240. doi: 10.4153/CMB-1981-037-1
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     title = {Essential {Extensions} of {T1-Spaces}},
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     year = {1981},
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     doi = {10.4153/CMB-1981-037-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1981-037-1/}
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