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In this paper, spaces with a locally countable sn-network are discussed. It is shown that a space with a locally countable sn-network iff it is an snf-countable space with a locally countable k-network. As its application, almost-open and closed mappings (or finite-to-one and closed mapping) preserve locally countable sn-networks, and a perfect preimage theorem on spaces with a locally countable sn-network is established.