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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.04939 |
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Table of Contents:
- 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.