Topological groups which satisfy an open mapping theorem

Douglas Lloyd Grant

Vol. 68 (1977), No. 2, 411–423

DOI: 10.2140/pjm.1977.68.411

Abstract

Let 𝒞 be a category of Hausdorff topological groups. A Hausdorff topological group G is called a B(𝒞) group if every continuous and almost open homomorphism from G onto a group in 𝒞 is open. An internal characterization of such groups is obtained. For certain 𝒞, the permanence properties of B(𝒞) groups and related categories are investigated, with some positive results pertaining to products and subobjects, and several counterexamples. Forms of the closed graph theorem for topological groups are then obtained which generalize results of T. Husain.

Mathematical Subject Classification 2000

Primary: 22A05

Secondary: 46A30, 54C10

Milestones

Received: 24 June 1974

Revised: 7 January 1977

Published: 1 February 1977