On the commutator subgroup of a nonconnected central group

In this paperG denotes a central topologicalT₂-group—G/Z(G) compact, whereZ(G) is the center. There are some results concerning compactness of the commutator subgroupG; in general (G)^– is compact ([3]), but not necessarilyG ([7]). If in additionG is a Lie group or ifG is connected,G is compact ([6], [5]). The purpose of this paper is to show, that if the componentG₀ of the identity is open,G must be compact, and to give an example of a compact group with (G/G₀) compact, whileG is not compact.Dedicated to Prof. R. Inzinger on his 70th birthday