تقرير
On Function Spaces Related to H-sober Spaces
| العنوان: | On Function Spaces Related to H-sober Spaces |
|---|---|
| المؤلفون: | Bao, Meng, Zhang, Xiaoyuan, Xu, Xiaoquan |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - General Topology, 54C35, 54D99, 06B30, 06B35 |
| الوصف: | In this paper, we mainly study the function spaces related to H-sober spaces. For an irreducible subset system H and $T_{0}$ spaces $X$ and $Y$, it is proved that $Y$ is H-sober iff the function space $\mathbb{C}(X, Y)$ of all continuous functions $f : X\longrightarrow Y$ equipped with the topology of pointwise convergence is H-sober iff the function space $\mathbb{C}(X, Y)$ equipped with the Isbell topology is H-sober. One immediate corollary is that for a $T_{0}$ space $X$, $Y$ is a sober space (resp., $d$-space, well-filtered space) iff the function space $\mathbb{C}(X, Y)$ equipped with the topology of pointwise convergence is a sober space (resp., $d$-space, well-filtered space) iff the function space $\mathbb{C}(X, Y)$ equipped with the the Isbell topology is a sober space (resp., $d$-space, well-filtered space). It is shown that $T_{0}$ spaces $X$ and $Y$, if the function space $\mathbb{C}(X, Y)$ equipped with the compact-open topology is H-sober, then $Y$ is H-sober. The function space $\mathbb{C}(X, Y)$ equipped with the Scott topology is also discussed. Comment: 11 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2204.08703 |
| رقم الأكسشن: | edsarx.2204.08703 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |