Chainability and Hemmingsen's Theorem

Authors

Taras Banakh, L'viv National University
Paul Bankston, Marquette UniversityFollow
Brian Raines, Baylor University
Wim Ruitenburg, Marquette UniversityFollow

Document Type

Article

Language

eng

Publication Date

8-1-2006

Publisher

Elsevier

Source Publication

Topology and its Applications

Source ISSN

0166-8641

Abstract

On the surface, the definitions of chainability and Lebesgue covering dimension ⩽1 are quite similar as covering properties. Using the ultracoproduct construction for compact Hausdorff spaces, we explore the assertion that the similarity is only skin deep. In the case of dimension, there is a theorem of E. Hemmingsen that gives us a first-order lattice-theoretic characterization. We show that no such characterization is possible for chainability, by proving that if κis any infinite cardinal and

Comments

Topology and its Applications, Vol. 153, No. 14 (August 1, 2006): 2462-2468. DOI.

Recommended Citation

Banakh, Taras; Bankston, Paul; Raines, Brian; and Ruitenburg, Wim, "Chainability and Hemmingsen's Theorem" (2006). Mathematics, Statistics and Computer Science Faculty Research and Publications. 610.
https://epublications.marquette.edu/mscs_fac/610