Chainability and Hemmingsen's Theorem
Topology and its Applications
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
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.