Abstract We deal with the problem of finding sufficient and necessary conditions on a generalized ordered space X under which for every compact space Y and for every separately continuous function f : X × Y → R : (a) f is of the first Baire class, i.e. X is a Moran space; (b) the function f is a pointwise limit of a sequence of continuous functions which is uniformly convergent to f with respect to each variable at every point of X × Y . We introduce PC- and wPC-properties of topological spaces and prove that wPC-property is equivalent to the perfectness in the class of GO-spaces, and every completely regular Moran Baire space has the wPC-property. We get a certain solution of the problem (b). In particular, we obtain that (b) is true for a perfect strongly zero-dimensional hereditarily Baire generalized ordered space X with G δ -diagonal. Moreover, under the assumption of the existence of the Souslin continuum (¬SH) we construct a Baire non-measurable separately continuous function f : X × Y → R defined on the product of a perfect linearly ordered paracompact space X and a compact space Y.

中文翻译：

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广义有序空间与紧空间积的分别连续函数的逼近和贝尔分类

摘要 我们处理在广义有序空间 X 上找到充要条件的问题，在该问题下，对于每个紧致空间 Y 和每个单独连续的函数 f : X × Y → R : (a) f 是第一 Baire 类，即 X 是 Moran 空间；(b) 函数 f 是连续函数序列的逐点极限，该序列对于 X × Y 的每个点处的每个变量一致收敛于 f。我们介绍了拓扑空间的PC-和wPC-性质，并证明wPC-性质等价于GO-空间类中的完美性，并且每一个完全正则的Moran Baire空间都具有wPC-性质。我们得到了问题 (b) 的某个解。特别地，我们得到 (b) 对于具有 G δ 对角线的完美强零维遗传贝雷广义有序空间 X 为真。