تقرير
Nowhere constant families of maps and resolvability
| العنوان: | Nowhere constant families of maps and resolvability |
|---|---|
| المؤلفون: | Juhász, István, van Mill, Jan |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - General Topology, 54A25, 54C30, 54D05 |
| الوصف: | If $X$ is a topological space and $Y$ is any set then we call a family $\mathcal{F}$ of maps from $X$ to $Y$ nowhere constant if for every non-empty open set $U$ in $X$ there is $f \in \mathcal{F}$ with $|f[U]| > 1$, i.e. $f$ is not constant on $U$. We prove the following result that improves several earlier results in the literature. If $X$ is a topological space for which $C(X)$, the family of all continuous maps of $X$ to $\mathbb{R}$, is nowhere constant and $X$ has a $\pi$-base consisting of connected sets then $X$ is $\mathfrak{c}$-resolvable. Comment: 6 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2312.12257 |
| رقم الأكسشن: | edsarx.2312.12257 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |