Skip to main content

A note on representable group topologies

Citations of this article
Mendeley users who have this article in their library.
Get full text


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 σ-compact and (locally) precompact groups which satisfy SRP.




Chis, C., Künzi, H. P. A., & Sanchis, M. (2020). A note on representable group topologies. In Studies in Systems, Decision and Control (Vol. 263, pp. 171–186). Springer.

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free