The range of maps on classical insertion theorems

Author: Yamazaki, Kaori

Source: Acta Mathematica Hungarica, Volume 132, Numbers 1-2, July 2011 , pp. 42-48(7)

Publisher: Springer

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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.

Keywords: insertion theorem; Banach lattice; topological vector lattice; 54C08; 54D15; 46A40

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s10474-011-0096-0

Affiliations: 1: Faculty of Economics, Takasaki City University of Economics, 1300 Kaminamie, Takasaki, Gunma, 370-0801, Japan, Email: kaori@tcue.ac.jp

Publication date: 2011-07-01