Leeman, Aaron, 1974-2010-03-012010-03-012009-06https://hdl.handle.net/1794/10227vii, 34 p. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number.We study the Bousfield localization functors known as [Special characters omitted], as described in [MahS]. In particular we would like to understand how they interact with suspension and how they stabilize. We prove that suitably connected [Special characters omitted]-acyclic spaces have suspensions which are built out of a particular type n space, which is an unstable analog of the fact that [Special characters omitted]-acyclic spectra are built out of a particular type n spectrum. This theorem follows Dror-Farjoun's proof in the case n = 1 with suitable alterations. We also show that [Special characters omitted] applied to a space stabilizes in a suitable way to [Special characters omitted] applied to the corresponding suspension spectrum.en-USChromatic functorsBousfield functorsAcyclic spacesSuspension spectrumAlgebraic topologyMathematicsThesis