The characterization for the sobriety of $L$-convex spaces
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866910648369152000 |
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| author | Wu, Guojun Yao, Wei |
| author_facet | Wu, Guojun Yao, Wei |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_09853 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The characterization for the sobriety of $L$-convex spaces Wu, Guojun Yao, Wei Category Theory General Topology 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. |
| title | The characterization for the sobriety of $L$-convex spaces |
| topic | Category Theory General Topology |
| url | https://arxiv.org/abs/2410.09853 |