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...Uc irvine electronic theses and dissertations title the cube problem for linear orders permalink https escholarship org item scfvf author ervin garrett theodore publication date copyright information this work is made available under terms of a creative commons attribution noncommercial noderivatives license availalbe at creativecommons licenses by nc nd peer reviewed thesis dissertation powered california digital library university submitted in partial satisfaction requirements degree doctorofphilosophy mathematics committee professor martin zeman chair matthew foreman svetlana jitomirskaya c tableofcontents page acknowledgments iv curriculumvitae v abstractofthedissertation vii introduction tail equivalence relations relation n preserving maps on isomorphism x analyzing bijections f preliminaries natural over class xovertheclassof topological spaces groups characterization terminology examples countable isomorphic to their squares asolution when has both endpoints asucient condition ...