On Baire property of spaces of compact-valued measurable functions
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912014759100416 |
|---|---|
| author | Osipov, Alexander V. |
| author_facet | Osipov, Alexander V. |
| contents | A topological space $X$ is Baire if the Baire Category Theorem holds for $X$, i.e., the intersection of any sequence of open dense subsets of $X$ is dense in $X$. One of the interesting problems in the theory of functional spaces is the characterization of the Baire property of a functional space through the topological property of the support of functions.
In the paper this problem is solved for the space $M(X, K)$ of all measurable compact-valued ($K$-valued) functions defined on a measurable space $(X,Σ)$ with the topology of pointwise convergence. It is proved that $M(X, K)$ is Baire for any metrizable compact space $K$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_02913 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Baire property of spaces of compact-valued measurable functions Osipov, Alexander V. General Topology A topological space $X$ is Baire if the Baire Category Theorem holds for $X$, i.e., the intersection of any sequence of open dense subsets of $X$ is dense in $X$. One of the interesting problems in the theory of functional spaces is the characterization of the Baire property of a functional space through the topological property of the support of functions. In the paper this problem is solved for the space $M(X, K)$ of all measurable compact-valued ($K$-valued) functions defined on a measurable space $(X,Σ)$ with the topology of pointwise convergence. It is proved that $M(X, K)$ is Baire for any metrizable compact space $K$. |
| title | On Baire property of spaces of compact-valued measurable functions |
| topic | General Topology |
| url | https://arxiv.org/abs/2409.02913 |