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• W2948296193 abstract "We study gaps in the lattice of (para)topological group topologies on a given abelian group and compare the properties of the topologies that form a gap. The emphasis is given to the study of (para)topological group topologies on the additive group of reals that constitute a gap with the usual topology of the reals. A number of examples are provided to show that several natural constructions produce gaps in the lattice of (para)topological group topologies on an abelian group. We also show that the weight, density, network weight and character of Hausdorff topological group topologies from a gap either coincide or the corresponding cardinal characteristic of the finer topology is not greater than that of the coarser topology. The article contains several open problems intended for a better understanding the lattices G(G) and PG(G) of topological and paratopological group topologies, respectively, on a given group G." @default.
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• W2948296193 date "2019-09-01" @default.
• W2948296193 modified "2023-09-23" @default.
• W2948296193 title "Gaps in lattices of (para)topological group topologies and cardinal functions" @default.
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• W2948296193 doi "https://doi.org/10.1016/j.topol.2019.06.006" @default.
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