The homotopic type of certain compact semigroups

  • A. M. Skryago


The relation between homotopic types of compact linearly connected semigroups and their minimal ideals is investigated. In Theorem 1 we prove that, if a semigroup has a homotopic unit, even if it is only one-sided, then the minimal ideal is a deformation retract of the semigroup and so is homotopically equivalent to the semigroup. In Theorem 2 it is proved that a Q-semigroup is weakly homotopically equivalent to its minimal ideal.


Homotopic Type Minimal Ideal Compact Semigroup Deformation Retract Homotopic Unit 
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Literature cited

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    K. H. Hofmann and P. S. Mostert, Elements of Compact Semigroups, Charles E. Merrill, Columbus (1966).Google Scholar
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    S. Ts. Hu, Homotopy Theory [in Russian], Moscow (1964).Google Scholar
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    A. L. Hudson, “Example of a nonacyclic continuum semigroup S with zero and S=ESE,” Proc. Amer. Math. Soc.,14, 648–653 (1963).Google Scholar
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    A. D. Wallace, “Cohomology, dimension and mobs,” Summa Brasil. Math.,3, 43–54 (1953).Google Scholar
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    A. D. Wallace, “Retractions in semigroups,” Pac. J. Math.,7, 1513–1517 (1957).Google Scholar

Copyright information

© Consultants Bureau 1971

Authors and Affiliations

  • A. M. Skryago
    • 1
  1. 1.Leningrad State Pedagogical InstituteUSSR

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