Version 1
: Received: 4 September 2021 / Approved: 6 September 2021 / Online: 6 September 2021 (10:09:59 CEST)
How to cite:
Tozzi, A. Disjoint Genus-0 Surfaces in Extremal Graph Theory and Set Theory Lead To a Novel Topological Theorem. Preprints2021, 2021090082. https://doi.org/10.20944/preprints202109.0082.v1
Tozzi, A. Disjoint Genus-0 Surfaces in Extremal Graph Theory and Set Theory Lead To a Novel Topological Theorem. Preprints 2021, 2021090082. https://doi.org/10.20944/preprints202109.0082.v1
Tozzi, A. Disjoint Genus-0 Surfaces in Extremal Graph Theory and Set Theory Lead To a Novel Topological Theorem. Preprints2021, 2021090082. https://doi.org/10.20944/preprints202109.0082.v1
APA Style
Tozzi, A. (2021). Disjoint Genus-0 Surfaces in Extremal Graph Theory and Set Theory Lead To a Novel Topological Theorem. Preprints. https://doi.org/10.20944/preprints202109.0082.v1
Chicago/Turabian Style
Tozzi, A. 2021 "Disjoint Genus-0 Surfaces in Extremal Graph Theory and Set Theory Lead To a Novel Topological Theorem" Preprints. https://doi.org/10.20944/preprints202109.0082.v1
Abstract
When an edge is removed, a cycle graph Cn becomes a n-1 tree graph. This observation from extremal set theory leads us to the realm of set theory, in which a topological manifold of genus-1 turns out to be of genus-0. Starting from these premises, we prove a theorem suggesting that a manifold with disjoint points must be of genus-0, while a manifold of genus-1 cannot encompass disjoint points.
Keywords
Combinatorics; Ramsey’s theory; Borsuk–Ulam theorem; black hole; singularity
Subject
Computer Science and Mathematics, Geometry and Topology
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
