Induced L-bornological vector spaces and L-Mackey convergence

Induced L-bornological vector spaces and L-Mackey convergence

Motivated by the concept of lattice-bornological vector spaces of J. Paseka, S. Solovyov and M. Stehlík, which extends bornological vector spaces to the fuzzy setting over a complete lattice, this paper continues to study the theory of L-bornological vector spaces. The specific description of L-born...

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Veröffentlicht in:Journal of intelligent & fuzzy systems 2021-01, Vol.40 (1), p.1277
Hauptverfasser: Zhen-yu, Jin, Cong-hua, Yan
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Convergence
Separation
Vector spaces
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description Motivated by the concept of lattice-bornological vector spaces of J. Paseka, S. Solovyov and M. Stehlík, which extends bornological vector spaces to the fuzzy setting over a complete lattice, this paper continues to study the theory of L-bornological vector spaces. The specific description of L-bornological vector spaces is presented, some properties of Lowen functors between the category of bornological vector spaces and the category of L-bornological vector spaces are discussed. In addition, the notions and some properties of L-Mackey convergence and separation in L-bornological vector spaces are showed. The equivalent characterization of separation in L-bornological vector spaces in terms of L-Mackey convergence is obtained in particular.
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subjects Convergence
Separation
Vector spaces
title Induced L-bornological vector spaces and L-Mackey convergence
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