The further study on the category of T-convergence groups

Lingqiang Li; Qiu Jin

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arXiv · 2409.04939

The further study on the category of T-convergence groups

Lingqiang Li·Qiu Jin

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Abstract

T-convergence groups is a natural extension of lattice-valued topological groups, which is a newly introduced mathematical structure. In this paper, we will further explore the theory of T-convergence groups. The main results include: (1) It possesses a novel characterization through the $\odot$-product of T-filters, and it is localizable, meaning that each T-convergence group is uniquely determined by the convergence at the identity element of the underlying group. (2) The definition of its subcategory, the topological T-convergence groups, can be simplified by removing the topological condition (TT). (3) It exhibits uniformization, which means that each T-convergence group can be reconstructed from a T-uniformly convergent space. (4) It possesses a power object, indicating that it has good category properties.

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BibTeX RIS

Lingqiang Li, Qiu Jin. 2024-09-08. The further study on the category of T-convergence groups. https://arxiv.org/abs/2409.04939

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