Abstract
In this work, the caliber of the space of subtle (thin) complete coupled (linked) systems of a topological space is studied. It is proved that an infinite cardinal \(\tau\) is a caliber for the space of subtle complete coupled systems \(N^{*}X\) of an infinite compact space \(X\), if and only if when cardinal \(\tau\) is a caliber for a subtle superextension \(\lambda^{*}X\) of the space \(X\). The weight and the Souslin number of the \(N_{\aleph_{0}}^{d}\)-kernel of the space \(X\) are also studied. It is shown that the weight of an infinite compact space \(X\) coincides with the weight of the \(N_{\aleph_{0}}^{d}\)-kernel of the space \(X\). It was also proved that the Souslin number of an infinite compact space \(X\) coincides with the Souslin number of the \(N_{\aleph_{0}}^{d}\)-kernel of the space \(X\).
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Yuldashev, T.K., Mukhamadiev, F.G. Caliber of Space of Subtle Complete Coupled Systems. Lobachevskii J Math 42, 3043–3047 (2021). https://doi.org/10.1134/S1995080221120398
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DOI: https://doi.org/10.1134/S1995080221120398