分离连续函数及其类似物的对角线
Diagonals of separately continuous functions and their analogs
摘要：
证明了对拓扑空间$X$、等连通空间$Z$和Bare-one映射$g:X\to Z$，存在一个具有对角$g$的独立连续映射$f:X^2\to Z$，即对每个$x\in X$都有$g(x)=f(x,x)$.在对$X$和$Z$的一个较弱的假设下，得到了分别连续映射$f:X^2\to Z$的对角线恰为Baire-1函数，对第一变元连续而对第二变元Lipschitz（可微）的映射$f:X^2\to Z$的对角线恰为稳定的第一Baire类函数.
英文摘要：
We prove that for a topological space $X$, an equiconnected space $Z$ and a Baire-one mapping $g:X\to Z$ there exists a separately continuous mapping $f:X^2\to Z$ with the diagonal $g$, i.e. $g(x)=f(x,x)$ for every $x\in X$. Under a mild assumptions on $X$ and $Z$ we obtain that diagonals of separately continuous mappings $f:X^2\to Z$ are exactly Baire-one functions, and diagonals of mappings $f:X^2\to Z$ which are continuous on the first variable and Lipschitz (differentiable) on the second one, are exactly the functions of stable first Baire class.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
