A Characterization of Affine Primal Topological Spaces Induced by Nilpotent Matrices

Ebner Pineda, Luis Mejías and Jorge Vielma

International Journal of Mathematics and Mathematical Sciences, 2025, vol. 2025, 1-8

Abstract: In this article, we prove that an n×n matrix A is nilpotent if and only if there exists an affine primal topology τ for Rn such that the space Rn,τ is both compact and connected. For τ being an affine primal topology, we mean that τ=U⊂Rn:f−1U⊂U, where f:Rn⟶Rn is a map defined by fx=Ax+p, with p∈Rn.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:5191108

DOI: 10.1155/ijmm/5191108

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