Minimal first countable spaces
1970 ◽
Vol 3
(1)
◽
pp. 55-64
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A topological space is E0 (resp. E1) provided every point is the countable intersection of neighborhoods (resp. closed neighborhoods). For i = 0 and i = 1, characterizations of minimal Ei. spaces (Ei. spaces with no strictly coarser Ei. topology) and Ei-closed spaces (Ei. spaces which are closed in every Ei. space containing them) are given; for example, the properties of minimal Ei. and minimal first countable Ti+1 are shown to be equivalent. Minimal E0 spaces are characterized as countable spaces with the cofinite topology, and minimal E1 spaces are characterized as E1-closed and semiregular spaces. E0-closed spaces are shown to be precisely the finite discrete spaces.
2007 ◽
Vol 59
(3)
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pp. 465-487
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Keyword(s):
2020 ◽
Vol 9
(3)
◽
pp. 1421-1431
Keyword(s):
2020 ◽
Vol 9
(7)
◽
pp. 5243-5249
2020 ◽
Keyword(s):
2019 ◽
Vol 7
(1)
◽
pp. 250-252
◽
Keyword(s):
2021 ◽
Vol 1941
(1)
◽
pp. 012025