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

We discuss the following Tkachuk’s question in the sense of ideal convergence: Is any Tychonoff connected sequential space a quotient image of a connected metric space? It is proved that let \mathcalI be an ideal on the set N then a topological space X is an \mathcalI_sn -connected space with an \mathcalI_sn -csf-network if and only if X is a continuous \mathcalI -covering image of a \mathcalI_sn\text- connected metric space. It follows that a topological space X is a connected \mathcalI_sn -sequential space with an \mathcalI_sn -csf-network if and only if X is a quotient \mathcalI -covering image of a \mathcalI_sn -connected metric space. Thus we partially resolved the problem raised by Tkachuk's.