On points of convergence lattices and sobriety for convergence spaces
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866909586715312128 |
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| author | Mynard, F. |
| author_facet | Mynard, F. |
| contents | We characterize the convergence spaces $(X,ξ)$ such that the space of points of $(\mathbb{P}X,\lim_ξ)$ in the category of convergence lattices is $(X,ξ)$. On the way, we study variants of sobriety and of the axiom $T_{D}$ in convergence spaces. New phenomena appear when leaving the realm of topological spaces. We obtain new hindsight into the space of points of a convergence lattice and study a special quotient of it, which, in the case $L=(\mathbb{P}X,\lim_ξ)$ for a topological space $(X,ξ)$, turns out to be homeomorphic to the sobrification of $X$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_10674 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On points of convergence lattices and sobriety for convergence spaces Mynard, F. General Topology 54A20 We characterize the convergence spaces $(X,ξ)$ such that the space of points of $(\mathbb{P}X,\lim_ξ)$ in the category of convergence lattices is $(X,ξ)$. On the way, we study variants of sobriety and of the axiom $T_{D}$ in convergence spaces. New phenomena appear when leaving the realm of topological spaces. We obtain new hindsight into the space of points of a convergence lattice and study a special quotient of it, which, in the case $L=(\mathbb{P}X,\lim_ξ)$ for a topological space $(X,ξ)$, turns out to be homeomorphic to the sobrification of $X$. |
| title | On points of convergence lattices and sobriety for convergence spaces |
| topic | General Topology 54A20 |
| url | https://arxiv.org/abs/2206.10674 |