Tightness type properties of spaces of quasicontinuous functions
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913718907961344 |
|---|---|
| author | Lipin, Anton E. Osipov, Alexander V. |
| author_facet | Lipin, Anton E. Osipov, Alexander V. |
| contents | Using approximation by continuous functions we prove the following statements to types of tightness in a space $Q_p(X, \mathbb{R})$ of all quasicontinuous real-valued functions with the topology $τ_p$ of pointwise convergence: the countability of tightness (fan-tightness, strong fan-tightness) at a point $f$ of space $Q_p(X, \mathbb{R})$ implies the countability of tightness (fan-tightness, strong fan-tightness) of space $Q_p(X,Y)$ of all quasicontinuous functions from $X$ into any non-one-point metrizable space $Y$. This result is the answer to the open question in the class of metrizable spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_04004 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tightness type properties of spaces of quasicontinuous functions Lipin, Anton E. Osipov, Alexander V. General Topology Classical Analysis and ODEs Using approximation by continuous functions we prove the following statements to types of tightness in a space $Q_p(X, \mathbb{R})$ of all quasicontinuous real-valued functions with the topology $τ_p$ of pointwise convergence: the countability of tightness (fan-tightness, strong fan-tightness) at a point $f$ of space $Q_p(X, \mathbb{R})$ implies the countability of tightness (fan-tightness, strong fan-tightness) of space $Q_p(X,Y)$ of all quasicontinuous functions from $X$ into any non-one-point metrizable space $Y$. This result is the answer to the open question in the class of metrizable spaces. |
| title | Tightness type properties of spaces of quasicontinuous functions |
| topic | General Topology Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2403.04004 |