Nearnesses and T0-Extensions of Topological Spaces
1983 ◽
Vol 26
(4)
◽
pp. 430-437
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AbstractIn [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.
2018 ◽
Vol 11
(3)
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pp. 882-892
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Keyword(s):
1961 ◽
Vol 13
◽
pp. 167-176
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2019 ◽
Vol 7
(1)
◽
pp. 250-252
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1970 ◽
Vol 67
(3)
◽
pp. 553-558
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2008 ◽
Vol 17
(05)
◽
pp. 579-599
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Keyword(s):
2021 ◽
Vol ahead-of-print
(ahead-of-print)
◽
2001 ◽
Vol 27
(8)
◽
pp. 505-512
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Keyword(s):
2004 ◽
Vol 2004
(70)
◽
pp. 3829-3837