# Talk:Space of mappings, topological

Indeed, consider $X=\R$ and $Y=[-1,1]$. If $S$ contains (at least one) non-compact set $A$, then $\mathfrak{T}$ is too strong, since there exists a continuous $f:X\to Y$ such that $f[A]\subseteq(0,1]$ and $\inf_{x\in A} f(x)=0$; the set of all continuous $g:X\to Y$ such that $g[A]\subseteq(0,1]$ does not contain $f-\varepsilon$, thus, is not a neighborhood of $f$ in the topology of uniform convergence. And if $S$ contains only compact sets, then $\mathfrak{T}$ is too weak, weaker than (or equal to) the compact-open topology, that is (in this case) the topology of locally uniform convergence. And the phrase "if $X\in S$, then $\mathfrak{T}$ is called..." in the article makes no sense, since it does not specify, what else is included into $S$. I propose to remove all that from the article. Boris Tsirelson (talk) 07:48, 30 December 2016 (CET)