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arXiv · 2410.09853

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

Guojun Wu·Wei Yao
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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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Guojun Wu, Wei Yao. 2024-10-13. The characterization for the sobriety of $L$-convex spaces. https://arxiv.org/abs/2410.09853

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