Generalized L-ˇCech closure operators and beyond
Abstract
In this paper, we first give a concrete example to illustrate that the construction of L-ˇCech closure operators given in [24, Theorem 3.1] fails to hold when L is a continuous residuated lattice. By strengthening L to be completely distributive, we propose two new kinds of operators, which are respectively called generalized closure operators and generalized L-closure operators, and establish the categorical relation between them. As an application, we prove the existence of a
Galois connection between the category of stratified generalized L-closure spaces and the category of stratified L-convex spaces. As a natural extension of probabilistic uniform spaces, we further introduce and study L-ˇCech uniform spaces, and also present their connection with L-ˇCech closure spaces.
Keywords
References
- 1] J. Adámek, H. Herrlich and G.E. Strecker, Abstract and Concrete Categories, Wiley, New York, 1990.
Details
Primary Language
English
Subjects
Mathematical Logic, Set Theory, Lattices and Universal Algebra, Topology
Journal Section
Research Article
Early Pub Date
December 30, 2025
Publication Date
December 30, 2025
Submission Date
August 13, 2025
Acceptance Date
November 8, 2025
Published in Issue
Year 2026 Number: Advanced Online Publication
APA
Dong, Y., Yi, S., & Li, G. (2025). Generalized L-ˇCech closure operators and beyond. Hacettepe Journal of Mathematics and Statistics, Advanced Online Publication. https://doi.org/10.15672/hujms.1763660
AMA
1.Dong Y, Yi S, Li G. Generalized L-ˇCech closure operators and beyond. Hacettepe Journal of Mathematics and Statistics. 2025;(Advanced Online Publication). doi:10.15672/hujms.1763660
Chicago
Dong, Yanyan, Shi Yi, and Gaolin Li. 2025. “Generalized L-ˇCech Closure Operators and Beyond”. Hacettepe Journal of Mathematics and Statistics, no. Advanced Online Publication. https://doi.org/10.15672/hujms.1763660.
EndNote
Dong Y, Yi S, Li G (December 1, 2025) Generalized L-ˇCech closure operators and beyond. Hacettepe Journal of Mathematics and Statistics Advanced Online Publication
IEEE
[1]Y. Dong, S. Yi, and G. Li, “Generalized L-ˇCech closure operators and beyond”, Hacettepe Journal of Mathematics and Statistics, no. Advanced Online Publication, Dec. 2025, doi: 10.15672/hujms.1763660.
ISNAD
Dong, Yanyan - Yi, Shi - Li, Gaolin. “Generalized L-ˇCech Closure Operators and Beyond”. Hacettepe Journal of Mathematics and Statistics. Advanced Online Publication (December 1, 2025). https://doi.org/10.15672/hujms.1763660.
JAMA
1.Dong Y, Yi S, Li G. Generalized L-ˇCech closure operators and beyond. Hacettepe Journal of Mathematics and Statistics. 2025. doi:10.15672/hujms.1763660.
MLA
Dong, Yanyan, et al. “Generalized L-ˇCech Closure Operators and Beyond”. Hacettepe Journal of Mathematics and Statistics, no. Advanced Online Publication, Dec. 2025, doi:10.15672/hujms.1763660.
Vancouver
1.Yanyan Dong, Shi Yi, Gaolin Li. Generalized L-ˇCech closure operators and beyond. Hacettepe Journal of Mathematics and Statistics. 2025 Dec. 1;(Advanced Online Publication). doi:10.15672/hujms.1763660