This thesis presents new theorems in homotopy theory, in particular it generalizes a theorem of Saharon Shelah. We employ a technique used by Janusz Pawlikowski to show that certain Peano continua have a least nontrivial homotopy group that is finitely presented or of cardinality continuum. We also use this technique to give some relative consistency results.
College and Department
Physical and Mathematical Sciences; Mathematics
BYU ScholarsArchive Citation
Corson, Samuel M., "Applications of Descriptive Set Theory in Homotopy Theory" (2010). All Theses and Dissertations. 2401.
compact metric space, descriptive set theory, homotopy theory