Spaces of Valuations
Spaces of Valuations
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DOI：
10.1111/j.1749-6632.1996.tb49168.x
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发表时间：
1996-12
影响因子：
5.2
通讯作者：
R. Heckmann
中科院分区：
文献类型：
--
作者：
R. Heckmann
赋值是将拓扑空间X的开集映射为正的真实的数的类测度函数。它们可以分为有限、点连续和Scott连续赋值。我们定义相应的赋值空间VfX <$VpX <$VX。本文的主要结果是：VpX是VpX的soberization，VpX是X上的自由sober局部凸拓扑锥。从这个普适性质，可以很容易地导出一个真实的值函数在Scott连续赋值上的积分的概念。该积分用于将空间VpX和VX表征为X上的某些真实的值函数空间的对偶空间。
Valuations are measurelike functions mapping the open sets of a topological space X into positive real numbers. They can be classified into finite, point continuous, and Scott continuous valuations. We define corresponding spaces of valuations VfX⊂ VpX⊂VX. The main results of the paper are that VpX is the soberification of VfX, and that VpX is the free sober locally convex topological cone over X. From this universal property, the notion of the integral of a real‐valued function over a Scott continuous valuation can be easily derived. The integral is used to characterize the spaces VpX and VX as dual spaces of certain spaces of real‐valued functions on X.