\mathcalI_sn\text- connected spaces and the images of metric spaces

We consider Tkachuk's question under ideal convergence. Namely, is every Tychonoff connected sequential space a quotient image of a connected metric space? We prove that, for an ideal \mathcalI on \mathbfN , a topological space X is an \mathcalI_sn\text- connected space with an \mathcalI_sn\text-csf\text- network if and only if X is the image of a continuous \mathcalI\text- sequence-covering mapping defined on an \mathcalI_sn\text- connected metric space. Consequently, a topological space X is a connected \mathcalI_sn\text- sequential space with an \mathcalI_sn\text-csf\text- network if and only if X is the image of a quotient \mathcalI\text- sequence-covering mapping defined on an \mathcalI_sn\text- connected metric space. This partially answers Tkachuk's question.