2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/222766This paper demonstrates the uniformly finite homology developed by Block and Weinberger and its relationship to amenable spaces via applications to the Cayley graph of Thompson's Group F. In particular, a certain class of subgraph of F is shown to be non-amenable. This shows that if F is amenable, these subsets (which include every finitely generated submonoid of the positive monoid of F) must necessarily have measure zero.pdfLaTex, 17 pages, 11 figuresGroup Theory20F65text