论文标题
从假发空间的产物中扩展映射
Extension of mappings from the product of pseudocompact spaces
论文作者
论文摘要
令$ x $和$ y $为假发空间，让功能$φ：x \ times y \ to \ mathbb r $分别连续。以下条件等效：（1）$ d \ subset y $的密集$g_δ$子集，因此$φ$在$ x \ times d $（namioka属性）的每个点是连续的； （2）$φ$是准确的； （3）$φ$扩展到$βx\ timesβy$的单独连续函数。该定理使得对Namioka特性的研究和eberlein-Grothendieck定理的概括是可能的，该定理是对功能空间子集的预发性的概括。我们还可以在几个伪造空间的乘积上分别进行连续函数的表征，该空间延伸到石材技术延伸的产物的分别连续功能。这些结果用于研究具有分别连续作战的小组和Mal'tSev空间。
Let $X$ and $Y$ be pseudocompact spaces and let the function $Φ: X\times Y\to \mathbb R$ be separately continuous. The following conditions are equivalent: (1) there is a dense $G_δ$ subset of $D\subset Y$ so that $Φ$ is continuous at every point of $X\times D$ (Namioka property); (2) $Φ$ is quasicontinuous; (3) $Φ$ extends to a separately continuous function on $βX\times βY$. This theorem makes it possible to combine studies of the Namioka property and generalizations of the Eberlein-Grothendieck theorem on the precompactness of subsets of function spaces. We also obtain a characterization of separately continuous functions on the product of several pseudocompact spaces extending to separately continuous functions on products of Stone-Cech extensions of spaces. These results are used to study groups and Mal'tsev spaces with separately continuous operations.
