Finiteness at infinity
1971 ◽
Vol 17
(4)
◽
pp. 299-304
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Keyword(s):
If X is a Tychonoff topological space, and if βX is the Stone-Cech compactification of X, then βX\X will denote the complement of X in βX. If A is a subset of X, then cl [A: X] will denote the closure of A in X, and int [A: X] will denote the interior of A in X. In Isbell ((3), p. 119) a property of βX\X is called a property which X has at infinity, and it is the aim of this paper to give necessary and sufficient conditions for X to be finite at infinity. Since βX is T1 we can say that if X is finite at infinity, then βX\X is closed in βX. So we lose nothing by restricting our attention to locally compact, Tychonoff spaces, and for the remainder of the paper X will denote such a space.
1996 ◽
Vol 19
(2)
◽
pp. 311-316
2013 ◽
Vol 88
(2)
◽
pp. 232-242
◽
1976 ◽
Vol 19
(4)
◽
pp. 487-494
◽
2013 ◽
Vol 21
(3)
◽
pp. 5-16
1988 ◽
Vol 37
(2)
◽
pp. 277-291
◽
1984 ◽
Vol 7
(4)
◽
pp. 663-666
◽
2015 ◽
Vol 23
(03)
◽
pp. 345-365
◽