Approximation theorems for compactifications

Kotaro Mine. "Approximation theorems for compactifications." Colloquium Mathematicae 122.1 (2011): 93-101. <http://eudml.org/doc/286261>.

@article{KotaroMine2011,
abstract = {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 $ℝ^\{n+1\}$. 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.},
author = {Kotaro Mine},
journal = {Colloquium Mathematicae},
keywords = {Compactification; Smirnov compactification; singular compactification; remainder; supremum of compactifications; unital Banach algebra},
language = {eng},
number = {1},
pages = {93-101},
title = {Approximation theorems for compactifications},
url = {http://eudml.org/doc/286261},
volume = {122},
year = {2011},
}

TY - JOUR
AU - Kotaro Mine
TI - Approximation theorems for compactifications
JO - Colloquium Mathematicae
PY - 2011
VL - 122
IS - 1
SP - 93
EP - 101
AB - 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 $ℝ^{n+1}$. 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.
LA - eng
KW - Compactification; Smirnov compactification; singular compactification; remainder; supremum of compactifications; unital Banach algebra
UR - http://eudml.org/doc/286261
ER -