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Forcing hereditarily separable compact-like group topologies on Abelian groupsDikranjan, Dikran N., 1950- ; Shakhmatov, DmitriLet ▫$\mathcal{C}$▫ denote the cardinality of the continuum. Using forcing we produce a modelof ZFC + CH with ▫$2^{\mathcal{C}}$▫ "arbitrarily large" and, in this model, obtain a characterization of ... the Abelian groups ▫$G$▫ (necessarily of size at most ▫$2^{\mathcal{C}}$▫) which admit: (i) a hereditarily separable group topology, (ii) a group topology making ▫$G$▫ into an ▫$S$▫-space, (iii) a hereditarily separable group topology that is either precompact, or pseudocompact, or countably compact (and which can be made to contain no infinite compact subsets), (iv) a group topology making ▫$G$▫ into an ▫$S$▫-space that is either precompact, or pseudocompact, or countably compact (and which also can be made without infinite compact subsets if necessary). As a by-product, we completely describe the algebraic structure of the Abelian groups of size at most ▫$2^{\mathcal{C}}$▫ which possess, at least consistently, a countably compact group topology (without infinite compact subsets, if desired). We also put to rest a 1980 problem of van Douwen about the cofinality of the size of countably compact Abelian groups.Source: Topology and its Applications. - ISSN 0166-8641 (Vol. 151, iss. 1-3, 2005, str. 2-54)Type of material - article, component partPublish date - 2005Language - englishCOBISS.SI-ID - 14086745
Author
Dikranjan, Dikran N., 1950- |
Shakhmatov, Dmitri
Topics
matematika |
topologija |
topološka grupa |
konvergentno zaporedje |
▫$S$▫-prostor |
mathematics |
topology |
topological group |
countably compact |
pseudocompact |
hereditarily separable |
convergent sequence |
▫$S$▫-space |
consistency results |
independence results |
forcing
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Dikranjan, Dikran N., 1950- | 28252 |
Shakhmatov, Dmitri | ![]() |
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