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- W3001587974 abstract "We study natural topologies in the sense of Debreu in the poset of topological group topologies on a topological group. We call this kind of topologies g-topologies. To be precise, groups admitting a non-totally disconnected g-natural topology as well as the non-totally disconnected g-topologies are identified. Moreover, the non-totally disconnected g-representable topologies as well as the total orders inducing non-totally disconnected group topologies are characterized. It is worth noting that our framework is more general than the usual one in representation theory: we assume no translation invariant properties. We also deal with some questions concerning order and topological algebra related to the semicontinuous representation property (SRP): we establish some results related to the Sorgenfrey line and SRP (some of them connected to the Proper Forcing Axiom (PFA)) and, we characterize (sigma )-compact and (locally) precompact groups which satisfy SRP." @default.
- W3001587974 created "2020-01-30" @default.
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- W3001587974 date "2020-01-01" @default.
- W3001587974 modified "2023-09-25" @default.
- W3001587974 title "A Note on Representable Group Topologies" @default.
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- W3001587974 doi "https://doi.org/10.1007/978-3-030-34226-5_8" @default.
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