Two topologies defined on some space are compatible if they contain in common a Hausdorff topology. The following result is proved for two compatible group topologies A 1 {\mathcal {A}_1} and A 2 {\mathcal {A}_{_2}} . Suppose A 1 {\mathcal {A}_1} is locally compact and A 2 {\mathcal {A}_2} is locally countably compact, and there is a non-void A 2 {\mathcal {A}_2} -open set contained in some A 1 {\mathcal {A}_1} -Lindelöf set. Then A 1 ⊆ A 2 {\mathcal {A}_1} \subseteq {\mathcal {A}_2} . This result is a stronger version of a theorem by Kasuga, in which two group topologies are shown to be equal if both of them are locally compact and σ \sigma -compact, and they are compatible.