Caliber of Space of Subtle Complete Coupled Systems

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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