On compact trees with the coarse wedge topology

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) . omega(0) is a Plichko space.

Keywords

• tree
• coarse wedge topology
• Valdivia compacta
• Plichko spaces