极小usco映射空间的局部与全局性质
Local and global properties of spaces of minimal usco maps
AI总结：
该文研究带紧集一致收敛拓扑的极小usco映射空间的局域与全局性质关联，刻画了其满足紧性、可度量化等7类性质的条件，补充了已有结果并得到极小cusco映射空间的类似刻画。
摘要：
本文研究了配备紧集上一致收敛拓扑的极小usco映射空间的局部性质与全局性质之间的相互作用。具体而言，对于每个局部紧空间$X$和度量空间$Y$，我们刻画了从$X$到$Y$的满足以下性质之一的极小usco映射空间：(i)紧性，(ii)局部紧性，(iii)$σ$-紧性，(iv)局部$σ$-紧性，(v)可度量化，(vi)ccc（可数链条件），(vii)局部ccc，其中在后两项中我们额外假设$Y$是可分且非离散的。上述部分结果补充了Ľubica Holá与Dušan Holý的研究成果。此外，我们还得到了极小cusco映射空间的类似刻画。
英文摘要：
In this paper, we study an interplay between local and global properties of spaces of minimal usco maps equipped with the topology of uniform convergence on compact sets. In particular, for each locally compact space $X$ and metric space $Y$, we characterize the space of minimal usco maps from $X$ to $Y$, satisfying one of the following properties: (i) compact, (ii) locally compact, (iii) $σ$-compact, (iv) locally $σ$-compact, (v) metrizable, (vi) ccc, (vii) locally ccc, where in the last two items we additionally assumed that $Y$ is separable and non-discrete. Some of the aforementioned results complement ones of Ľubica Holá and Dušan Holý. Also, we obtain analogical characterizations for spaces of minimal cusco maps.
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