Rechtstopologische Intervallhalbgruppen und Kreishalbgruppen
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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 ). 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 , Lawson ). 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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