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

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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() ... continued below

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iv, 31 pages

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Dahal, Koshal Raj August 2015.

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This dissertation is part of the collection entitled: UNT Theses and Dissertations and was provided by UNT Libraries to Digital Library, a digital repository hosted by the UNT Libraries. It has been viewed 24 times . More information about this dissertation can be viewed below.

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  • Dahal, Koshal Raj

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Description

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.

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iv, 31 pages

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UNT Theses and Dissertations

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  • August 2015

Added to The UNT Digital Library

  • March 4, 2016, 4:14 p.m.

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  • April 24, 2017, 6:34 a.m.

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Dahal, Koshal Raj. Trees and Ordinal Indices in C(K) Spaces for K Countable Compact, dissertation, August 2015; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc804883/: accessed July 21, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .