Geodesic
Products of ultrafilters and maximal linked systems on widely understood measurable spaces
Ural mathematical journal, Tome 7 (2021) no. 2, pp. 3-32

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Constructions related to products of maximal linked systems (MLSs) and MLSs on the product of widely understood measurable spaces are considered (these measurable spaces are defined as sets equipped with $\pi$-systems of their subsets; a $\pi$-system is a family closed with respect to finite intersections). We compare families of MLSs on initial spaces and MLSs on the product. Separately, we consider the case of ultrafilters. Equipping set-products with topologies, we use the box-topology and the Tychonoff product of Stone-type topologies. The properties of compaction and homeomorphism hold, respectively.
Keywords: maximal linked system, topology, ultrafilter. 
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     author = {Alexander G. Chentsov},
     title = {Products of ultrafilters and maximal linked systems on widely understood measurable spaces},
     journal = {Ural mathematical journal},
     pages = {3--32},
     publisher = {mathdoc},
     volume = {7},
     number = {2},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UMJ_2021_7_2_a0/}
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Alexander G. Chentsov. Products of ultrafilters and maximal linked systems on widely understood measurable spaces. Ural mathematical journal, Tome 7 (2021) no. 2, pp. 3-32. http://geodesic.mathdoc.fr/item/UMJ_2021_7_2_a0/