# Article

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Keywords:
\$k\$-space; \$k\$-network; closed map; compact-covering map
Summary:
We prove some closed mapping theorems on \$k\$-spaces with point-countable \$k\$-networks. One of them generalizes La\v snev's theorem. We also construct an example of a Hausdorff space \$Ur\$ with a countable base that admits a closed map onto metric space which is not compact-covering. Another our result says that a \$k\$-space \$X\$ with a point-countable \$k\$-network admitting a closed surjection which is not compact-covering contains a closed copy of \$Ur\$.
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