The categories of $L$-convex spaces and $L$-convergence spaces: extensionality and productivity of quotient maps

Year 2025, Volume: 54 Issue: 4, 1257 - 1275, 29.08.2025

Xiancheng Han Bin Pang

https://doi.org/10.15672/hujms.1543634

Cited By: 1

Abstract

Based on a complete residuated lattice $L$, we show that the category of $L$-convex spaces is not extensional and is closed under the formation of finite products of quotient maps. Then we propose the concept of (preconcave, concave) $L$-convergence spaces via $L$-co-Scott closed sets and prove that the category of concave $L$-convergence spaces is isomorphic to that of $L$-concave spaces. Finally, we investigate the categorical properties of $L$-convergence spaces and show that it is extensional and closed under the formation of finite products of quotient maps.

Keywords

L-convex space , L-concave space , L-convergence space , extensionality , quotient map

Project Number

the Natural Science Foundation of China (Nos. 12471428, 12071033, 12271036)

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