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We study the set of periods of degree 1 continuous maps from σ into itself,where σ denotes the space shaped like the letter σ (i.e.,a segment attachedto a circle by one of its endpoints).Since the maps under consideration havedegree 1,the rotation theory can be used.We show that,when the interior ofthe rotation interval contains an integer,then the set of periods (of periodicpoints of any rotation number) is the set of all integers except maybe 1 or 2.