$σ$-Continuous functions and related cardinal characteristics of the continuum

Year, pages: 2020, 1 - 10

A function $f:X\to Y$ between topological spaces is called {\em $σ$-continuous} (resp. {\em $\barσ$-continuous}) if there exists a (closed) cover $\{X_n\}_n\in\w$ of $X$ such that for every $n\in\w$ the restriction $f{\restriction}X_n$ is continuous. By $\sig$ (resp. $\bsig$) we denote the largest cardinal $κ≤\mathfrak c$ such that every function $f:X\to\IR$ defined on a subset $X\subset\IR$ of cardinality $|X| < κ$ is $σ$-continuous (resp. $\barσ$-continuous). It is clear that $\w₁≤\bsig≤\sig≤\mathfrak c$. We prove that $\mathfrak p≤\mathfrak q₀=\bsig=\min\{\sig,\mathfrak b,\mathfrak q\}≤\sig≤\min\{\non(\mathcal M),\non(\mathcal N)\}$.

Banakh, T. 2020. $σ$-Continuous functions and related cardinal characteristics of the continuum. In Tatra Mountains Mathematical Publications, vol. 76, no.2, pp. 1-10. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2019-0014

Banakh, T. (2020). $σ$-Continuous functions and related cardinal characteristics of the continuum. Tatra Mountains Mathematical Publications, 76(2), 1-10. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2019-0014

Publisher: Mathematical Institute, Slovak Academy of Sciences, Bratislava

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