分离连续多值映射的对角
Diagonals of separately continuous multi-valued mappings
摘要：
本文解决了一个关于构造具有给定对角线的分离连续映射的问题，该对角线是等连通空间中取值的连续映射序列的逐点极限。我们构造了一个例子，闭值分别连续映射$f:[0,1]^2\to \mathbb R$具有处处不连续的对角线。实例表明，关于紧值分离连续映射的联合连续点集的结果不能推广到闭值映射的情况。
英文摘要：
We solve a problem on a construction of a separately continuous mapping with the given diagonal, which is the pointwise limit of a sequence of continuous mappings valued in an equiconnected space. We construct an example of a closed-valued separately continuous mapping $f:[0,1]^2\to \mathbb R$ with an everywhere discontinuous diagonal. The example shows that the results on the joint continuity point set of compact-valued separately continuous mappings can not be generalized to the case of closed-valued mappings.
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