Topology

2101 Submissions

[2] viXra:2101.0113 [pdf] submitted on 2021-01-18 07:07:04

Each Topological Space X is of the Form Aut(y)\y

Authors: Pierre-Yves Gaillard
Comments: 4 Pages.

We show that for each topological space X there is a topological space Y such that the quotient space G\Y of Y by the action of the automorphism group G of Y is homeomorphic to X.
Category: Topology

[1] viXra:2101.0005 [pdf] submitted on 2021-01-01 12:21:36

Lack of Disjointness in Genus-1 Surfaces: The Punctured Balloon Theorem

Authors: Arturo Tozzi
Comments: 4 Pages.

Take a balloon, that is a genus-one manifold. If you break the jointness by piercing its surface, the hole gest lost and the punctured balloon becomes a genus-0 manifold. Starting from this trivial claim, we prove a topological theorem which plainly states that “the ends of a donut can meet, whilst the ends of a kidney pie cannot”. In this succinct note, we discuss the theorem and its implications in disparate topics such as topological connectedness, gauge theories and the physics of the black holes.
Category: Topology