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Weak Hausdorff Gaps and the ≤ t Problem

✍ Scribed by Kyriakos Keremedis

Book ID
102942647
Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
604 KB
Volume
45
Category
Article
ISSN
0044-3050

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✦ Synopsis

We find topological characterizations of the pseudointersection number p and the tower number t of the real line and we show that p < tiff there exists a compact separable Tz space X of *-weight < p that can be covered by < t nowhere dense sets iff there exists a weak Hausdorff gap of size n < t, i. e., a pair ( { A ,

is a family of pseudointersections of A, and there is no pseudointersection S of A meeting each member of B in an infinite set.

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## Abstract We consider the problem of finding __u__ ∈ __L__ ^2^(__I__ ), __I__ = (0, 1), satisfying ∫~__I__~ __u__ (__x__ )__x__ d__x__ = __μ__ ~__k__~ , where __k__ = 0, 1, 2, …, (__α__ ~__k__~ ) is a sequence of distinct real numbers greater than –1/2, and **__μ__** = (__μ__ ~__kl__~ ) is a g