On the probabilistic metrizability of approach spaces
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917835819712512 |
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| author | Lai, Hongliang Shen, Lili Yu, Junche |
| author_facet | Lai, Hongliang Shen, Lili Yu, Junche |
| contents | We investigate approach spaces generated by probabilistic metric spaces with respect to a continuous t-norm $*$ on the unit interval $[0,1]$. Let $k^*$ be the supremum of the idempotent elements of $*$ in $[0,1)$. It is shown that if $k^*=1$ (resp. $k^*<1$), then an approach space is probabilistic metrizable with respect to $*$ if and only if it is probabilistic metrizable with respect to the minimum (resp. product) t-norm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_07548 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the probabilistic metrizability of approach spaces Lai, Hongliang Shen, Lili Yu, Junche General Topology Category Theory 54A05, 54E70, 54E35 We investigate approach spaces generated by probabilistic metric spaces with respect to a continuous t-norm $*$ on the unit interval $[0,1]$. Let $k^*$ be the supremum of the idempotent elements of $*$ in $[0,1)$. It is shown that if $k^*=1$ (resp. $k^*<1$), then an approach space is probabilistic metrizable with respect to $*$ if and only if it is probabilistic metrizable with respect to the minimum (resp. product) t-norm. |
| title | On the probabilistic metrizability of approach spaces |
| topic | General Topology Category Theory 54A05, 54E70, 54E35 |
| url | https://arxiv.org/abs/2408.07548 |