Combinatorial Topology: A Theorem

Author

Charles Nagy

Date of Defense

6-1964

Department

Mathematics

Abstract

Discusses a theorem and its proof: Let R be a compact metric space ∑={G₀,G₁,...,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.
https://scholarworks.wmich.edu/honors_theses/287

Access Setting

Honors Thesis-Campus Only