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Topological Features of Topological Groups

  • Chapter
Handbook of the History of General Topology

Part of the book series: History of Topology ((HIPO,volume 3))

Abstract

Our aim is to give a relatively concise description of the state-of-the-art in the theory of topological groups up to the moment. The paper we present is addressed primarily to the General Topology-inclined reader, and this partly explains the choice of the title. The second reason for speaking of topological features of topological groups is that we focus our attention on topological ideas and methods in the area and almost completely omit the very rich and profound algebraic part of the theory of locally compact groups (except for a brief discussion in Sections 2.4 and 2.5). Neither do we have any intention of presenting material concerning the representation theory of (locally) compact groups — the book [We4] by Weil and Section 5 of [Pon4] by Pontryagin are recommended in this respect.

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  1. Universidad Autónoma Metropolitana, Mexico

    Michael G. Tkachenko

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  1. Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, USA

    C. E. Aull

  2. Department of Mathematics and Computer Science, University of Antwerp, RUCA, Antwerp, Belgium

    R. Lowen

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Tkachenko, M.G. (2001). Topological Features of Topological Groups. In: Aull, C.E., Lowen, R. (eds) Handbook of the History of General Topology. History of Topology, vol 3. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0470-0_5

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