Beyond Lebesgue and Baire IV: density topologies and a converse Steinhaus-Weil theorem

Bingham, N. H. and Ostaszewski, Adam (2018) Beyond Lebesgue and Baire IV: density topologies and a converse Steinhaus-Weil theorem. Topology and its Applications, 239. pp. 274-292. ISSN 0166-8641

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Abstract

The theme here is category-measure duality, in the context of a topological group. One can often handle the (Baire) category case and the (Lebesgue,or Haar) measure cases together, by working bi-topologically: switching between the original topology and a suitable refinement (a density topology). This prompts a systematic study of such density topologies, and the corresponding Ó-ideals of negligibles. Such ideas go back to Weil's classic book, and to Hashimoto's ideal topologies. We make use of group norms, which cast light on the interplay between the group and measure structures. The Steinhaus-Weil interior-points theorem ('on AA¯1´) plays a crucial role here; so too does its converse, the Simmons-Mospan theorem.

Item Type:	Article
Official URL:	https://www.journals.elsevier.com/indagationes-mat...
Additional Information:	© 2017 The Authors
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	04 Dec 2017 11:30
Last Modified:	08 Apr 2024 06:42
URI:	http://eprints.lse.ac.uk/id/eprint/85937

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