FMF, Mathematical Library, Lj. (MAKLJ)
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Chains of pseudocompact group topologiesDikranjan, Dikran N., 1950-We show that for several large classes of groups ▫$G$▫, the poset ▫$\mathscr{P}_\sigma(G)$▫ of all pseudocompact group topologies of weight $\sigma$ on ▫$G$▫ contains a poset isomorphic to the power ... set of ▫$\sigma$▫ whenever ▫$\mathscr{P}_\sigma(G) \ne \emptyset$▫. This permits to describe in purely set-theoretic terms when ▫$G$▫ has bounded (from above) chains of pseudocompact group topologies of weight ▫$\sigma$▫. Moreover, we show that these topologies may additionally have some of the following properties: linear (in particular, zero-dimensional), connected and locally connected, disconnected and locally connected, connected and nonlocally connected, etc. It turns out that the question of whether the cardinality of unbounded chains of pseudocompact group topologies of weight ▫$\omega_1$▫ on ▫$\mathbb{R}$▫ is larger than that of bounded ones cannot be answered in ZFC. We answer also questions posed by Comfort and Remus (1994) on pseudocompact topologization of a given weight.Source: Journal of Pure and Applied Algebra. - ISSN 0022-4049 (Vol. 124, iss. 1, 1998, str. 65-100)Type of material - article, component partPublish date - 1998Language - englishCOBISS.SI-ID - 16249433
Author
Dikranjan, Dikran N., 1950-
Topics
matematika |
topološke grupe |
veriga |
delno urejena množica |
mathematics |
topological groups |
chain |
poset |
pseudocompact group topologies
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Dikranjan, Dikran N., 1950- | 28252 |
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