Tychonoff空间上自由对象的o-有界性
o-Boundedness of free objects over a Tychonoff space
摘要：
本文利用Tychonoff空间X的性质刻画了自由交换拓扑群F（X）（A（X））和自由局部凸线性拓扑空间L（X）的[严格] o-有界性。这些性质似乎接近所谓的选择原则，这使我们能够表明，（这是一致的ZFC）的性质Hurewicz（门格尔）是l-不变的。给出了具有强组合性质的OF-待定拓扑群的一种构造方法。
英文摘要：
In this paper we characterize [strict] o-boundedness of the free (abelian) topological group F(X) (A(X)) as well as the free locally-convex linear topological space L(X) in terms of properties of a Tychonoff space X. These properties appear to be close to so-called selection principles, which permits us to show, that (it is consistent with ZFC that) the property of Hurewicz (Menger) is l-invariant. This gives a method of construction of OF-undetermined topological groups with strong combinatorial properties.
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