On compact trees with the coarse wedge topology
Volume 253 / 2020
Studia Mathematica 253 (2020), 283-306
MSC: Primary 46B26, 46A50; Secondary 54D30, 06A06.
DOI: 10.4064/sm190115-20-3
Published online: 30 December 2019
Abstract
We investigate the class of compact trees, endowed with the coarse wedge topology, in connection with the area of non-separable Banach spaces. We describe Valdivia compact trees in terms of inner structures and we characterize the space of continuous functions on them. Moreover we prove that the space of continuous functions on an arbitrary tree with height less than $\omega _1\cdot \omega _0$ is a Plichko space.
