Approximation theorems for compactifications

• Autorzy: Kotaro Mine
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46J10: Banach algebras of continuous functions, function algebras
• 54D40: Remainders
• 54D35: Extensions of spaces (compactifications, supercompactifications, completions, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2011
• Tom: 122
• Numer: 1
• Strony: 93-101

Daty

wydano

2011

Twórcy

autor

Kotaro Mine

• Institute of Mathematics, University of Tsukuba, Tsukuba, 305-8571, Japan

Identyfikatory

DOI

10.4064/cm122-1-9