Acta Mathematica Hungarica
Volume/Issue:
Volume 132: Issue 1-2
The range of maps on classical insertion theorems
Author: Kaori Yamazaki 1
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  • 1 Faculty of Economics, Takasaki City University of Economics, 1300 Kaminamie, Takasaki, Gunma, 370-0801, Japan
DOI:
https://doi.org/10.1007/s10474-011-0096-0
Page Count:
42–48
Publication Date:
01 Jul 2011
Online Publication Date:
10 Mar 2011
Article Category:
Research Article
Restricted access

Abstract

A classical insertion theorem due to Katětov–Tong (or Dowker–Katětov, Michael) reads that ℝ can be a test space for the range of maps on the insertion theorem which characterizes the domain to be normal (or normal and countably paracompact, perfectly normal). It is known that the range ℝ in the Katětov–Tong insertion theorem is not necessarily replaced by a non-trivial separable Banach lattice. We show that the range ℝ in the Dowker–Katětov and Michael insertion theorems can be replaced by any non-trivial separable Banach lattice.

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Cover Acta Mathematica Hungarica
Acta Mathematica Hungarica
Print ISSN:
0236-5294
Online ISSN:
1588-2632
Keywords:
insertion theorem; Banach lattice; topological vector lattice; 54C08; 54D15; 46A40

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