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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.04004 |
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Table of 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.