In this thesis, we provide constructive proofs of serveral generalizations of Sperner's Lemma, a combinatorial result which is equivalent to the Brouwer Fixed Point Theorem. This lemma makes a statement about the number of a certain type of simplices in the triangulation of a simplex with a special labeling. We prove generalizations for polytopes with simplicial facets, for arbitrary 3-polytopes, and for polygons. We introduce a labeled graph which we call a nerve graph to prove these results. We also suggest a possible non-constructive proof for a polytopal generalization.
Identifer | oai:union.ndltd.org:CLAREMONT/oai:scholarship.claremont.edu:hmc_theses-1127 |
Date | 01 May 2000 |
Creators | Peterson, Elisha |
Publisher | Scholarship @ Claremont |
Source Sets | Claremont Colleges |
Detected Language | English |
Type | text |
Format | application/pdf |
Source | HMC Senior Theses |
Page generated in 0.0013 seconds