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On compact trees with the coarse wedge topology

Volume 253 / 2020

Jacopo Somaglia Studia Mathematica 253 (2020), 283-306 MSC: Primary 46B26, 46A50; Secondary 54D30, 06A06. DOI: 10.4064/sm190115-20-3 Published online: 30 December 2019


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.


  • Jacopo SomagliaDipartimento di Matematica
    Università degli Studi di Milano
    Via C. Saldini, 50
    20133 Milano MI, Italy
    Department of Mathematical Analysis
    Faculty of Mathematics and Physics
    Charles University
    Sokolovská 83
    186 75 Praha 8, Czech Republic

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