Lattice representation of L-quasi-convex spaces
Abstract
Based on a complete Heyting algebra L, we first propose the concept of L-quasi-convex spaces and construct an adjunction between the category of L-S 0-quasi-convex spaces and the opposite category of complete L-ordered sets. Then we present the concept of weakly fuzzy algebraic lattices and prove that an L-quasi-convex structure endowed with the fuzzy inclusion order is precisely a weakly fuzzy algebraic lattice. Secondly, we introduce the notion of sobriety in Lquasi-convex spaces from the perspective of categorical equivalence, showing that the category of sober L-quasi-convex spaces is dually equivalent to that of weakly fuzzy algebraic lattices. Finally, we construct a monad on the category of L-S 0-quasi-convex spaces and obtain that the Eilenberg–Moore algebras of this m onad are precisely sober L-quasi-convex spaces.
Keywords
Project Number
the Natural Science Foundation of China (Nos. 12471428, 12071033, 12271036)
References
- [1] J. Adámek, H. Herrlich and G.E. Strecker, Abstract and Concrete Categories, Wiley, New York, 1990.
Details
Primary Language
English
Subjects
Topology
Journal Section
Research Article
Early Pub Date
December 30, 2025
Publication Date
December 30, 2025
Submission Date
July 13, 2025
Acceptance Date
November 20, 2025
Published in Issue
Year 2026 Number: Advanced Online Publication
APA
Sun, L., & Pang, B. (2025). Lattice representation of L-quasi-convex spaces. Hacettepe Journal of Mathematics and Statistics, Advanced Online Publication. https://doi.org/10.15672/hujms.1741223
AMA
1.Sun L, Pang B. Lattice representation of L-quasi-convex spaces. Hacettepe Journal of Mathematics and Statistics. 2025;(Advanced Online Publication). doi:10.15672/hujms.1741223
Chicago
Sun, Licong, and Bin Pang. 2025. “Lattice Representation of L-Quasi-Convex Spaces”. Hacettepe Journal of Mathematics and Statistics, no. Advanced Online Publication. https://doi.org/10.15672/hujms.1741223.
EndNote
Sun L, Pang B (December 1, 2025) Lattice representation of L-quasi-convex spaces. Hacettepe Journal of Mathematics and Statistics Advanced Online Publication
IEEE
[1]L. Sun and B. Pang, “Lattice representation of L-quasi-convex spaces”, Hacettepe Journal of Mathematics and Statistics, no. Advanced Online Publication, Dec. 2025, doi: 10.15672/hujms.1741223.
ISNAD
Sun, Licong - Pang, Bin. “Lattice Representation of L-Quasi-Convex Spaces”. Hacettepe Journal of Mathematics and Statistics. Advanced Online Publication (December 1, 2025). https://doi.org/10.15672/hujms.1741223.
JAMA
1.Sun L, Pang B. Lattice representation of L-quasi-convex spaces. Hacettepe Journal of Mathematics and Statistics. 2025. doi:10.15672/hujms.1741223.
MLA
Sun, Licong, and Bin Pang. “Lattice Representation of L-Quasi-Convex Spaces”. Hacettepe Journal of Mathematics and Statistics, no. Advanced Online Publication, Dec. 2025, doi:10.15672/hujms.1741223.
Vancouver
1.Licong Sun, Bin Pang. Lattice representation of L-quasi-convex spaces. Hacettepe Journal of Mathematics and Statistics. 2025 Dec. 1;(Advanced Online Publication). doi:10.15672/hujms.1741223