#### Date of Defense

6-1964

#### Department

Mathematics

#### Abstract

Discusses a theorem and its proof: Let R be a compact metric space ∑={G_{0},G_{1},...,Gk} an open ε-covering of R, � the nerve of this covering, and K a geometric realization of ⱵK in some Euclidean space R^{m}, so that to each set G_{i} of ∑ there corresponds a point c_{i} (an element of R^{m}) which is a vertex of the geometric nerve K of the covering ∑. Then there exists a continuous ε-mapping f of the space R into polyhedron |K| for which x ε G_{p} implies that f(x) is contained in a simplex A* of K with vertex c_{p}.

#### Recommended Citation

Nagy, Charles, "Combinatorial Topology: A Theorem" (1964). *Honors Theses*. 287.

http://scholarworks.wmich.edu/honors_theses/287

#### Access Setting

Honors Thesis-Campus Only