Majorants, Uniformities, and $bo-$Convergence in $L-$Scaled Spaces
Abstract
This article investigates the relations between uniform continuity and $bo$-convergence in $L$-scaled spaces, which are ultrametric spaces with distances measured using elements from a lattice $L$ with the smallest element. The $bo$-convergence in $L$-scaled spaces is defined by means of the order convergence in the lattice $L.$ We examine how monotone majorants can be employed to bound the behavior of functions and their iterates in these spaces. A central result demonstrates that if a function is uniformly continuous on an $L$-scaled space, then images of $bo$-convergent sequences have $bo$-convergent subsequences. Several results related to the uniform structure of $L$-scaled spaces and dominated operators are presented.
Keywords
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References
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Details
Primary Language
English
Subjects
Mathematical Logic, Set Theory, Lattices and Universal Algebra, Topology
Journal Section
Research Article
Authors
Publication Date
December 30, 2025
Submission Date
January 10, 2025
Acceptance Date
June 13, 2025
Published in Issue
Year 2025 Volume: 17 Number: 2
APA
Gezer, N. A. (2025). Majorants, Uniformities, and $bo-$Convergence in $L-$Scaled Spaces. Turkish Journal of Mathematics and Computer Science, 17(2), 304-309. https://doi.org/10.47000/tjmcs.1617617
AMA
1.Gezer NA. Majorants, Uniformities, and $bo-$Convergence in $L-$Scaled Spaces. TJMCS. 2025;17(2):304-309. doi:10.47000/tjmcs.1617617
Chicago
Gezer, Niyazi Anil. 2025. “Majorants, Uniformities, and $bo-$Convergence in $L-$Scaled Spaces”. Turkish Journal of Mathematics and Computer Science 17 (2): 304-9. https://doi.org/10.47000/tjmcs.1617617.
EndNote
Gezer NA (December 1, 2025) Majorants, Uniformities, and $bo-$Convergence in $L-$Scaled Spaces. Turkish Journal of Mathematics and Computer Science 17 2 304–309.
IEEE
[1]N. A. Gezer, “Majorants, Uniformities, and $bo-$Convergence in $L-$Scaled Spaces”, TJMCS, vol. 17, no. 2, pp. 304–309, Dec. 2025, doi: 10.47000/tjmcs.1617617.
ISNAD
Gezer, Niyazi Anil. “Majorants, Uniformities, and $bo-$Convergence in $L-$Scaled Spaces”. Turkish Journal of Mathematics and Computer Science 17/2 (December 1, 2025): 304-309. https://doi.org/10.47000/tjmcs.1617617.
JAMA
1.Gezer NA. Majorants, Uniformities, and $bo-$Convergence in $L-$Scaled Spaces. TJMCS. 2025;17:304–309.
MLA
Gezer, Niyazi Anil. “Majorants, Uniformities, and $bo-$Convergence in $L-$Scaled Spaces”. Turkish Journal of Mathematics and Computer Science, vol. 17, no. 2, Dec. 2025, pp. 304-9, doi:10.47000/tjmcs.1617617.
Vancouver
1.Niyazi Anil Gezer. Majorants, Uniformities, and $bo-$Convergence in $L-$Scaled Spaces. TJMCS. 2025 Dec. 1;17(2):304-9. doi:10.47000/tjmcs.1617617