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 Val- divia compact trees in terms of inner structures and we characterize the space of contin- uous functions on them. Moreover we prove that the space of continuous functions on an arbitrary tree with height less than ω1 · ω0 is a Plichko space.
On compact trees with the coarse wedge topology / J. Somaglia. - In: STUDIA MATHEMATICA. - ISSN 0039-3223. - 2020:253(2020), pp. 283-306. [10.4064/sm190115-20-3]
On compact trees with the coarse wedge topology
J. Somaglia
2020
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 Val- divia compact trees in terms of inner structures and we characterize the space of contin- uous functions on them. Moreover we prove that the space of continuous functions on an arbitrary tree with height less than ω1 · ω0 is a Plichko space.
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