Geodesic
Products of ultrafilters and irresolvable spaces
Sbornik. Mathematics, Tome 19 (1973) no. 1, pp. 105-115 
V. I. Malykhin. Products of ultrafilters and irresolvable spaces. Sbornik. Mathematics, Tome 19 (1973) no. 1, pp. 105-115. http://geodesic.mathdoc.fr/item/SM_1973_19_1_a6/
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Voir la notice de l'article provenant de la source Math-Net.Ru

A space dense in itself is said to be $k$-resolvable if there exists a system of cardinality $k$ of disjoint dense subsets. The main results of the paper can be formulated as follows: 1. If there exists a countably-centered free ultrafilter, then there are dense in themselves $T_1$-spaces whose product is irresolvable. 2. Any sets $X$ and $Y$ support irresolvable $T_1$-topologies whose product is maximally resolvable. 3. Assuming the continuum hypothesis, an ultrafilter whose cartesian square is dominated by only three ultrafilters is constructed on a countable set. 4. If a set of uncountable cardinality supports an ultrafilter whose square is dominated by exactly three ultrafilters, then its cardinality is measurable. A number of problems are posed. Bibliography: 9 titles.

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[7] F. P. Ramsey, “On a problem of formal logic”, Proc. London Math. Soc., 30 (1930), 262–286 | DOI

[8] W. Rudin, “Homogenity problems in theory of Čech compactifications”, Duke Math. J., 23:3 (1956), 409–423 | DOI | MR

[9] J. Juhasz, A. Verbeek, N. S. Kroonenberg, Cardinal functions in topology, Math. Centre Tracts., 34, Amsterdam, 1971 | MR | Zbl