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In this paper, we establish the locally diffeomorphic property of thesolution to McKean-Vlasov stochastic differential equations defined on theEuclidean space. Our approach is built upon the insightful ideas put forth byKunita. We observe that although the coefficients satisfy the global Lipschitzcondition and some suitable regularity condition, the solution in general doesnot satisfy the globally homeomorphic property at any time except the initialtime, which sets McKean-Vlasov stochastic differential equations apartsignificantly from classical stochastic differential equations. Finally, weprovide an example to complement our results.

The locally homeomorphic property of McKean-Vlasov SDEs under the global Lipschitz condition