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Trees and Ordinal Indices in C(K) Spaces for K Countable Compact

In the dissertation we study the C(K) spaces focusing on the case when K is countable compact and more specifically, the structure of C() spaces for < ω1 via special type of trees that they contain. The dissertation is composed of three major sections. In the first section we give a detailed proof of the theorem of Bessaga and Pelczynski on the isomorphic classification of C() spaces. In due time, we describe the standard bases for C(ω) and prove that the bases are monotone. In the second section we consider the lattice-trees introduced by Bourgain, Rosenthal and Schechtman in C() spaces, and define rerooting and restriction of trees. The last section is devoted to the main results. We give some lower estimates of the ordinal-indices in C(ω). We prove that if the tree in C(ω) has large order with small constant then each function in the root must have infinitely many big coordinates. Along the way we deduce some upper estimates for c0 and C(ω), and give a simple proof of Cambern's result that the Banach-Mazur distance between c0 and c = C(ω) is equal to 3.

Identiferoai:union.ndltd.org:unt.edu/info:ark/67531/metadc804883
Date08 1900
CreatorsDahal, Koshal Raj
ContributorsSari, Bunyamin, Jackson, Stephen, Gao, Su
PublisherUniversity of North Texas
Source SetsUniversity of North Texas
LanguageEnglish
Detected LanguageEnglish
TypeThesis or Dissertation
Formativ, 31 pages, Text
RightsPublic, Dahal, Koshal Raj, Copyright, Copyright is held by the author, unless otherwise noted. All rights Reserved.

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