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manuscripta mathematica

, Volume 14, Issue 2, pp 183–193 | Cite as

Rechtstopologische Intervallhalbgruppen und Kreishalbgruppen

  • Wolfgang Ruppert
Article

Abstract

It is well known that in a topological semigroup S with an identity 1 the maximal subgroup H (1) must be open if 1 has an euclidean neighborhood (Mostert-Shields [7]). If multiplication in S is only “separately” continuous, i.e. x↦yx and x↦xy is continuous for all y∈S, the statement remains true if the underlying space of S is a compact manifold (Berglund [2], Lawson [6]). In this paper the case of a compact semigroup with only one-sided continuity (i.e. x↦yx or x↦xy is continuous for all y∈S) which is defined on an interval or a circle is investigated. It is also shown that a group, defined on the line or on a circle, must be a topological group if it satisfies this very weak condition.

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Literatur

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Copyright information

© Springer-Verlag 1974

Authors and Affiliations

  • Wolfgang Ruppert
    • 1
  1. 1.Lehrkanzel für Mathematik und Darstellende Geometrie Hochschule für Bodenkultur in WienWien

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