The characterization for the sobriety of $L$-convex spaces

Document Type : Research Paper

Authors

Nanjing University of Information Science and Technology

Abstract

With a commutative integral quantale $L$ as the truth value table, this study focuses on the characterizations of the sobriety of stratified $L$-convex spaces, as introduced by Liu and Yue in 2024. It is shown that a stratified sober $L$-convex space $Y$ is a sobrification of a stratified $L$-convex space $X$ if and only if there exists a quasihomeomorphism from $X$ to $Y$; a stratified $L$-convex space is sober if and only if it is a strictly injective object in the category of stratified $S_0$ $L$-convex spaces.

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References

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Iranian Journal of Fuzzy Systems
Volume 21, Issue 6
November and December 2024
Pages 55-68

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