manuscripta mathematica

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

Rechtstopologische Intervallhalbgruppen und Kreishalbgruppen

  • Wolfgang Ruppert


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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  1. [1]
    BERGLUND, J.F.: Compact connected ordered semitopological semigroups. J. London math. Soc., II.Ser.,4, 533–540, (1972)Google Scholar
  2. [2]
    BERGLUND, J.F.: Semitopological semigroups on circles. J. London math. Soc., II. Ser.5, 395–398, (1972)Google Scholar
  3. [3]
    CLIFFORD, A.H., and PRESTON, G.B.: The algebraic theory of semigroups I. Math. Surveys 7 (Amer. Math. Soc., Providence, 1961)Google Scholar
  4. [4]
    ELLIS, R.: Locally compact transformation groups. Duke math. J.24, 119–126, (1957)Google Scholar
  5. [5]
    HOFMANN, K.H., and MOSTERT, P.S.: Elements of compact semigroups. (1. Aufl. Columbus, Ohio, C.E. Merrill, 1966)Google Scholar
  6. [6]
    LAWSON, J.D.: Joint continuity in semitopological semigroups, abstract in Amer.math.Soc., Notices20, (1973)Google Scholar
  7. [7]
    MOSTERT, P.S., and SHIELDS, A.L.: Semigroups with identity on a manifold. Trans.Amer.math.Soc.91, 380–389,(1959)Google Scholar
  8. [8]
    RUPPERT, W.: Rechtstopologische Halbgruppen. J. reine angew. Math.261, 123–133, (1973)Google Scholar

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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