Geodesic
Nearnesses and T0 -Extensions of Topological Spaces
Canadian mathematical bulletin, Tome 26 (1983) no. 4, pp. 430-437

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DOI

In [3], Reed establishes a bijection between the (equivalence classes of) principal T1 -extensions of a topological space X and the compatible, cluster-generated, Lodato nearnesses on X. We extend Reed's result to the T0 case by obtaining a one-to-one correspondence between the principal T0 -extensions of a space X and the collections of sets (called “t-grill sets”) which generate a certain class of nearnesses which we call “t-bunch generated” nearnesses. This correspondence specializes to principal T0-compactifications. Finally, we show that there is a bijection between these t-grill sets and the filter systems of Thron [5], and that the corresponding extensions are equivalent.
DOI : 10.4153/CMB-1983-071-4
Mots-clés : 54E17, 54A05, 54C20, 54D10, 54D35, Principal, T0 -extension, nearness, t -Lodato, grill, t-bunch generated, t-grill set, compactification, contigual, compatible, Lodato, cluster 
Dean, Alice M. Nearnesses and T0 -Extensions of Topological Spaces. Canadian mathematical bulletin, Tome 26 (1983) no. 4, pp. 430-437. doi: 10.4153/CMB-1983-071-4
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     author = {Dean, Alice M.},
     title = {Nearnesses and {T0} {-Extensions} of {Topological} {Spaces}},
     journal = {Canadian mathematical bulletin},
     pages = {430--437},
     year = {1983},
     volume = {26},
     number = {4},
     doi = {10.4153/CMB-1983-071-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1983-071-4/}
}
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