o-Boundedness of free objects over a Tychonoff space
نویسنده
چکیده
In this paper we characterize various sorts of 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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Real Analysis Quals - Helpful Information
2.1. Basic properties: separation, countability, separability, compactness, connectedness. A space X is Tychonoff if for u, v ∈ X, there exists a neighborhood of u not containing v (and by symmetry a neighborhood of v not containing u). It is Hausdorff if every two points can be separated by disjoint neighborhoods. It is regular if it is Tychonoff and every closed set and point not in the set c...
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تاریخ انتشار 2005