Ostaszewski, Adam (2013) Beyond Lebesgue and Baire III: Steinhausʼ theorem and its descendants. Topology and Its Applications, 160 (10). pp. 1144-1154. ISSN 0166-8641
We generalize from the real line to normed groups (i.e., the invariantly metrizable, right topological groups) a result on infinite combinatorics, valid for 'large' subsets in both the category and measure senses, which implies both Steinhaus's Theorem and many of its descendants. We deduce the inherent measure-category duality in this setting directly from properties of analytic sets. We apply the result to extend the Pettis Theorem and the Continuous Homomorphism Theorem to normed groups, i.e., beyond metrizable topological groups, and in a companion paper deduce automatic joint-continuity results for group operations.
|Additional Information:||© 2013 The Author|
|Library of Congress subject classification:||Q Science > QA Mathematics|
|Sets:||Departments > Mathematics|
|Date Deposited:||16 May 2013 12:31|
Actions (login required)
|Record administration - authorised staff only|