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

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.
Date: August 2015
Creator: Dahal, Koshal Raj
Partner: UNT Libraries

[Biology Building and Chemistry Building exteriors]

Description: Photograph of the Biology Building (left) and the Chemistry Building (center) from the sidewalk in front of them. There are small plants lining the walk up to the Biology Building and larger shrubs and a tree in front of the Chemistry Building. Several cars and a truck are parked along the street in front of the two buildings.
Date: 197u
Location Info:
Partner: UNT Libraries Special Collections

[Biology Building and Chemistry Building from street]

Description: Photograph of the Biology Building (left) and the Chemistry Building (right) from the street in front of them. There are small plants lining the walk up to the Biology Building and larger shrubs and a tree in front of the Chemistry Building. There are some cars parked in front of the two buildings on the street.
Date: 197u
Location Info:
Partner: UNT Libraries Special Collections

[Information Science Library]

Description: Photograph of the Information Science Library from the lawn in front of it. Bushes line the base of the exterior wall and there are several trees on the grounds. Tied between one of the trees and a telephone pole is a sign announcing an upcoming event. Another sign is leaning against the same tree.
Date: 196u
Partner: UNT Libraries Special Collections

[Psychology Building entrance]

Description: Photograph of the Psychology Building entrance. A large staircase bordered by hedges leads up to the doors. A large tree stands in front of the stairs and a bush is beside them. A flagpole is standing at the top of the building.
Date: 197u
Location Info:
Partner: UNT Libraries Special Collections

[Journalism Building exterior]

Description: Photograph of the exterior of the Journalism Building. There are bushes around the entrance to the building and a bench is set up against the wall. Trees are growing further back along the building and cars are lined up parked on the curb.
Date: 196u
Location Info:
Partner: UNT Libraries Special Collections

[Bruce Hall north entrance]

Description: Photograph of the north entrance of Bruce Hall. The entrance is decorated with two lamps and shrubs are growing along the base of the walls. Above the doorway is a balcony with open doors. There are several trees by the building and cars are parked along the roadside in front of it.
Date: 197u
Location Info:
Partner: UNT Libraries Special Collections

[Bruce Hall from across street]

Description: Photograph of the north entrance of Bruce Hall. The entrance is decorated with two lamps and shrubs are growing along the base of the walls. There are several trees by the building and cars are parked along the roadside in front of it.
Date: 197u
Location Info:
Partner: UNT Libraries Special Collections

[Psychology Building exterior front]

Description: Photograph of the Psychology Building entrance. A large divided staircase bordered by hedges leads up to the doors. A large tree stands next to the stairs and other bushes are around them. A flagpole is standing at the top of the building.
Date: 197u
Location Info:
Partner: UNT Libraries Special Collections

[Administration Building from street]

Description: Photograph of the Administration Building. A flagpole is standing in front of the building. Three women are passing by the stairs leading to the building and another is standing on the curb. Cars are parked in the spots beside her and another is driving towards her. There is landscaping all around the building.
Date: 197u
Location Info:
Partner: UNT Libraries Special Collections