Geodesic
Extensive Subcategories of the Category of T 1-spaces
Canadian journal of mathematics, Tome 27 (1975) no. 2, pp. 311-318

Voir la notice de l'article provenant de la source Cambridge University Press

It is well known that epimorphisms in the category Top (Top1, respectively) of topological spaces (T0spaces, respectively) and continuous maps are precisely onto continuous maps. Since every mono-reflective subcategory of a category is also epi-reflective and every embedding in Top (Top1, respectively) is a monomorphism, there is no nontrivial reflective subcategory of Top (Top1 respectively) such that every reflection is an embedding. However, in the category Top0 of T 0-spaces and continuous maps as well as in the category Haus of Hausdorff spaces and continuous maps, there are epimorphisms which are not onto. Moreover, every reflection of a reflective subcategory of Top0, which contains a non T1 -space, is an embedding [16]. 
Hong, Sung Sa. Extensive Subcategories of the Category of T 1-spaces. Canadian journal of mathematics, Tome 27 (1975) no. 2, pp. 311-318. doi: 10.4153/CJM-1975-037-7
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