| dc.creator | Badiger, Chidanand | |
| dc.creator | Venkatesh, T. | |
| dc.date | 2023-03-27 | |
| dc.date.accessioned | 2023-05-11T20:42:05Z | |
| dc.date.available | 2023-05-11T20:42:05Z | |
| dc.identifier | https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/4533 | |
| dc.identifier | 10.22199/issn.0717-6279-4533 | |
| dc.identifier.uri | https://revistaschilenas.uchile.cl/handle/2250/225557 | |
| dc.description | In this paper, we give new topological invariants and a complete characterization to homeomorphisms. The finding a sufficient condition for homeomorphism and classifying topological spaces up to homeomorphism is the open problemin topology [1, 9, 14]. In this article, the main results are Propositions 3.24, 4.40 and 4.41, and Propositions 4.40 is about complete characterization of homeomorphisms i.e. "f : M -->N is a homeomorphism if and only if f# : pi1M --> pi1N is a groupoid iso-homeomorphism". this is the answer to the open problem [1, 9, 14] mentioned. First, we characterize the homeomorphisms completely. In addition, we resolve the open issue [1, 9, 14] of finding sufficient conditions for two topological spaces to be homeomorphic by giving an invariant. The entire result will be obtained by constructing a new notion, that is an extension of fundamental groups; which is already a topological invariant but not a sufficient one. We extend new theory by defining an algebraic sense of fundamental groupoid by establishing such algebraic structure and a unique topology on it. This fundamental groupoid is different from the fundamental groupoid in [16] and also these two different groupoids (one is algebraic sense and another is category theoretic) are not equivalent. We have an explicit description for algebraic structure groupoid and a unique topological structure on fundamental groupoid. And also we will discuss their topological properties also possibility of smooth structures. | en-US |
| dc.format | application/pdf | |
| dc.language | eng | |
| dc.publisher | Universidad Católica del Norte. | en-US |
| dc.relation | https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/4533/4254 | |
| dc.rights | Copyright (c) 2023 Chidanand Badiger, T. Venkatesh | en-US |
| dc.rights | https://creativecommons.org/licenses/by/4.0 | en-US |
| dc.source | Proyecciones (Antofagasta, On line); Vol. 42 No. 2 (2023); 273-302 | en-US |
| dc.source | Proyecciones. Revista de Matemática; Vol. 42 Núm. 2 (2023); 273-302 | es-ES |
| dc.source | 0717-6279 | |
| dc.source | 10.22199/issn.0717-6279-2023-02 | |
| dc.subject | groupoid | en-US |
| dc.subject | fundamental group | en-US |
| dc.subject | fundamental groupoid | en-US |
| dc.subject | topological groupoid | en-US |
| dc.subject | induced homomorphism | en-US |
| dc.subject | bundle | en-US |
| dc.subject | 14F35 | en-US |
| dc.subject | 18F15 | en-US |
| dc.subject | 55Q05 | en-US |
| dc.title | A kind of characterization of homeomorphism and homeomorphic spaces by Core fundamental groupoid: a good invariant | en-US |
| dc.type | info:eu-repo/semantics/article | |
| dc.type | info:eu-repo/semantics/publishedVersion | |
| dc.type | Peer-reviewed Article | en-US |
| dc.type | text | en-US |
| dc.coverage | 1600-till | en-US |
