We shall show several approximation theorems for the Hausdorff compactifications of metrizable spaces or locally compact Hausdorff spaces. It is shown that every compactification of the Euclidean n-space ℝⁿ is the supremum of some compactifications homeomorphic to a subspace of . Moreover, the following are equivalent for any connected locally compact Hausdorff space X: (i) X has no two-point compactifications, (ii) every compactification of X is the supremum of some compactifications whose remainder is homeomorphic to the unit closed interval or a singleton, (iii) every compactification of X is the supremum of some singular compactifications. We shall also give a necessary and sufficient condition for a compactification to be approximated by metrizable (or Smirnov) compactifications.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm122-1-9,
author = {Kotaro Mine},
title = {Approximation theorems for compactifications},
journal = {Colloquium Mathematicae},
volume = {122},
year = {2011},
pages = {93-101},
zbl = {1222.54030},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm122-1-9}
}
Kotaro Mine. Approximation theorems for compactifications. Colloquium Mathematicae, Tome 122 (2011) pp. 93-101. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm122-1-9/