For separable metrizable spaces $X,Y$ and a metrizable topological group $Z$ by $S(X×Y,Z)$  we denote the space of all separately continuous functions $f: X×Y→Z$  endowed with the topology of fiberwise uniform convergence, generated by the subbase consisting of the sets $[K_X × K_Y, U] = \{f ∈ S(X×Y,Z)) : f(K_X × K_Y⊂U \},$ where $U$ is an open subset of $Z$ and $K_X⊂X, K_Y⊂Y$ are compact sets one of which is a singleton. We prove that every separately continuous function $f: X×Y→Z$ with zero-dimensional image $f(X×Y)$  is a limit of a sequence of jointly continuous functions in the topology of fiberwise uniform convergence.

[1] Voloshin G.A., Maslyuchenko V.K. Topologization of the space of non-narrowly continuous functions // Karp. math. publ. - 2013. - 5 , № 2. - P. 199-207.

[2] Voloshin G.A., Maslyuchenko V.K. On linear interpolation of vector-valued functions and its application // Mat. Studii. - 2014. -42 , № 2. - P. 129-133.

[3] Voloshyn G.A., Masliuchenko V.K. Sequential closure of the space of jointly continuous functions in the space of differentially continuous functions .

[4] Voloshin G.A., Maslyuchenko V.K., Maslyuchenko O.V. On the layerwise uniform approximation of non-narrowly continuous functions by polynomials // Mat. Bulletin of the NTS. - 2013. - 10.- P. 135-158.

[5] Voloshin G.A., Maslyuchenko V.K., Maslyuchenko O.V. Embedding of a space of non-negatively continuous functions in the product of Banach spaces and its barrel-valuedness // Mat. Bulletin of the NTS. - 2014. - 11. - P. 36-50.

[6]  Arhangel'skii A., Tkachenko M. Topological groups and related structures. - Atlantis Studies in Mathematics, 1. Atlantis Press, Paris; World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2008.

[7]  Dugundji J. An extension of Tietze's theorem // Pacific J. Math. - 1951. - 1 . P. 353-367.

[8]  Engelking R. General Topology. - Heldermann Verlag, Berlin, 1989.