Abstract
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.
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Translated from Matematicheskie Zametki, Vol. 8, No. 6, pp. 711–719, December, 1970.
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Skryago, A.M. The homotopic type of certain compact semigroups. Mathematical Notes of the Academy of Sciences of the USSR 8, 872–876 (1970). https://doi.org/10.1007/BF01673686
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DOI: https://doi.org/10.1007/BF01673686