Approximation theorems for compactifications
Colloquium Mathematicum, Tome 122 (2011) no. 1, pp. 93-101.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 $\mathbb R^n$ is the supremum of some compactifications homeomorphic to a subspace of $\mathbb R^{n+1}$. 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.
DOI : 10.4064/cm122-1-9
Keywords: shall several approximation theorems hausdorff compactifications metrizable spaces locally compact hausdorff spaces shown every compactification euclidean n space mathbb supremum compactifications homeomorphic subspace mathbb moreover following equivalent connected locally compact hausdorff space nbsp has two point compactifications every compactification supremum compactifications whose remainder homeomorphic unit closed interval singleton iii every compactification supremum singular compactifications shall necessary sufficient condition compactification approximated metrizable smirnov compactifications

Kotaro Mine 1

1 Institute of Mathematics University of Tsukuba Tsukuba, 305-8571, Japan
@article{10_4064_cm122_1_9,
     author = {Kotaro Mine},
     title = {Approximation theorems for compactifications},
     journal = {Colloquium Mathematicum},
     pages = {93--101},
     publisher = {mathdoc},
     volume = {122},
     number = {1},
     year = {2011},
     doi = {10.4064/cm122-1-9},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/cm122-1-9/}
}
TY  - JOUR
AU  - Kotaro Mine
TI  - Approximation theorems for compactifications
JO  - Colloquium Mathematicum
PY  - 2011
SP  - 93
EP  - 101
VL  - 122
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/cm122-1-9/
DO  - 10.4064/cm122-1-9
LA  - en
ID  - 10_4064_cm122_1_9
ER  - 
%0 Journal Article
%A Kotaro Mine
%T Approximation theorems for compactifications
%J Colloquium Mathematicum
%D 2011
%P 93-101
%V 122
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/cm122-1-9/
%R 10.4064/cm122-1-9
%G en
%F 10_4064_cm122_1_9
Kotaro Mine. Approximation theorems for compactifications. Colloquium Mathematicum, Tome 122 (2011) no. 1, pp. 93-101. doi : 10.4064/cm122-1-9. http://geodesic.mathdoc.fr/articles/10.4064/cm122-1-9/

Cité par Sources :