On the $c_0$-extension property for compact lines

Abstract

We present a characterization of the continuous increasing surjections $\varphi :K\to L$ between compact lines $K$ and $L$ for which the corresponding subalgebra ${\varphi }^{\ast }C(L)$ has the $c_0$-extension property in $C(K)$. A natural question arising in connection with this characterization is shown to be independent of the axioms of ZFC.

12 pages

References in corpus (3)

• Complementation in Spaces of Continuous Functions on Compact Lines
• Compact lines and the Sobczyk property
• The structure of Valdivia compact lines