Acta Mathematica Hungarica

, Volume 132, Issue 1, pp 42–48

The range of maps on classical insertion theorems

Article

DOI: 10.1007/s10474-011-0096-0

Cite this article as:
Yamazaki, K. Acta Math Hung (2011) 132: 42. doi:10.1007/s10474-011-0096-0

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.

Key words and phrases

insertion theorem Banach lattice topological vector lattice 

2000 Mathematics Subject Classification

54C08 54D15 46A40 

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2011

Authors and Affiliations

  1. 1.Faculty of EconomicsTakasaki City University of EconomicsTakasakiJapan

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