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Primal Topologies on Finite-Dimensional Vector Spaces Induced by Matrices

Author

Listed:
  • Luis Mejías
  • Jorge Vielma
  • Ã ngel Guale
  • Ebner Pineda
  • Sergejs Solovjovs

Abstract

Given an matrix A, considered as a linear map A:℠n⟶℠n, then A induces a topological space structure on ℠n which differs quite a lot from the usual one (induced by the Euclidean metric). This new topological structure on ℠n 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 ℠n by matrices; in particular, we describe geometrical properties of the respective spaces for the case.

Suggested Citation

  • Luis Mejías & Jorge Vielma & à ngel Guale & Ebner Pineda & Sergejs Solovjovs, 2023. "Primal Topologies on Finite-Dimensional Vector Spaces Induced by Matrices," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2023, pages 1-7, January.
    • Handle: RePEc:hin:jijmms:9393234
    DOI: 10.1155/2023/9393234
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    Cited by:

    1. Hanan Al-Saadi & Huda Al-Malki, 2024. "Categories of Open Sets in Generalized Primal Topological Spaces," Mathematics, MDPI, vol. 12(2), pages 1-14, January.

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