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arXiv · 2403.04004

Tightness type properties of spaces of quasicontinuous functions

Anton E. Lipin·Alexander V. Osipov
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Abstract

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.

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Anton E. Lipin, Alexander V. Osipov. 2025-03-05. Tightness type properties of spaces of quasicontinuous functions. https://arxiv.org/abs/2403.04004

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