Countable Compagtifications
Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 616-620
Voir la notice de l'article provenant de la source Cambridge University Press
It is assumed that all topological spaces discussed in this paper are Hausdorff. By a compactification αX of a space X we mean a compact space containing X as a dense subspace. If, for some positive integer n, αX — X consists of n points, we refer to αX as an n-point compactification of X, in which case we use the notation αn X. If αX — X is countable, we refer to αX as a countable compactification of X. In this paper, the statement that a set is countable means that its elements are in one-to-one correspondence with the natural numbers. In particular, finite sets are not regarded as being countable. Those spaces with n-point compactifications were characterized in (3). From the results obtained there it followed that the only n-point compactifications of the real line are the well-known 1- and 2-point compactifications and the only n-point compactification of the Euclidean N-space, EN (N > 1), is the 1-point compactification.
Jr., Kenneth D. Magill. Countable Compagtifications. Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 616-620. doi: 10.4153/CJM-1966-060-6
@article{10_4153_CJM_1966_060_6,
author = {Jr., Kenneth D. Magill},
title = {Countable {Compagtifications}},
journal = {Canadian journal of mathematics},
pages = {616--620},
year = {1966},
volume = {18},
number = {1},
doi = {10.4153/CJM-1966-060-6},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1966-060-6/}
}
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