Primal Topologies on Finite-Dimensional Vector Spaces Induced by Matrices

Autor: Luis Mejías, Jorge Vielma, Ángel Guale, Ebner Pineda
Jazyk: angličtina
Rok vydání: 2023
Předmět:
Zdroj: International Journal of Mathematics and Mathematical Sciences, Vol 2023 (2023)
Druh dokumentu: article
ISSN: 1687-0425
DOI: 10.1155/2023/9393234
Popis: Given an matrix A, considered as a linear map A:ℝn⟶ℝn, then A induces a topological space structure on ℝn which differs quite a lot from the usual one (induced by the Euclidean metric). This new topological structure on ℝn has very interesting properties with a nice special geometric flavor, and it is a particular case of the so called “primal space,” In particular, some algebraic information can be shown in a topological fashion and the other way around. If X is a non-empty set and f:X⟶X is a map, there exists a topology τf induced on X by f, defined by τf=U⊂X:f−1U⊂U. The pair X,τf is called the primal space induced by f. In this paper, we investigate some characteristics of primal space structure induced on the vector space ℝn by matrices; in particular, we describe geometrical properties of the respective spaces for the case.
Databáze: Directory of Open Access Journals
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