Maximal linked systems on products of widely understood measurable spaces. (Russian. English summary) Zbl 1488.54038
Summary: Maximal linked systems (MLS) of sets on widely understood measurable spaces (MS) are considered; in addition, every such MS is realized by equipment of a nonempty set with a \(\pi \)-system of its subsets with “zero” and “unit” (\(\pi \)-system is a nonempty family of sets closed with respect to finite intersections). Constructions of the MS product connected with two variants of measurable (in wide sense) rectangles are investigated. Families of MLS are equipped with topologies of the Stone type. The connection of product of above-mentioned topologies considered for box and Tychonoff variants and the corresponding (to every variant) topology of the Stone type on the MLS set for the MS product is studied. The properties of condensation and homeomorphism for resulting variants of topological equipment are obtained.
MSC:
| 54B10 | Product spaces in general topology |
| 54A10 | Several topologies on one set (change of topology, comparison of topologies, lattices of topologies) |
| 54B05 | Subspaces in general topology |
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