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1.
One of the most celebrated results in the theory of hyperspaces says that if the Vietoris topology on the family of all nonempty closed subsets of a given space is normal, then the space is compact (Ivanova-Keesling-Velichko). The known proofs use cardinality arguments and are long. In this paper we present a short proof using known results concerning Hausdorff uniformities. 相似文献
2.
A. N. Gavryushkin 《Algebra and Logic》2007,46(3):149-157
We construct an example of a theory with a finite (greater than one) number of isomorphism types of countable models such
that its prime and saturated models have computable presentations and there exists a model which lacks in such.
Supported by the Council for Grants (under RF President) and State Aid of Fundamental Science Schools via project NSh-4413.2006.1.
__________
Translated from Algebra i Logika, Vol. 46, No. 3, pp. 275–289, May–June, 2007. 相似文献
3.
We give a self‐contained proof of the preservation theorem for proper countable support iterations known as “tools‐preservation”, “Case A” or “first preservation theorem” in the literature. We do not assume that the forcings add reals. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
4.
D. H. Fremlin R. A. Johnson E. Wajch 《Proceedings of the American Mathematical Society》1996,124(9):2897-2903
A space Borel multiplies with a space if each Borel set of is a member of the -algebra in generated by Borel rectangles. We show that a regular space Borel multiplies with every regular space if and only if has a countable network. We give an example of a Hausdorff space with a countable network which fails to Borel multiply with any non-separable metric space. In passing, we obtain a characterization of those spaces which Borel multiply with the space of countable ordinals, and an internal necessary and sufficient condition for to Borel multiply with every metric space.
5.
M. W. Warner 《Fuzzy Sets and Systems》1989,30(3):321-327
An amended proof of a theorem of Franklin's on sequentiality and sequential compactness is presented, and a corresponding fuzzy version formulated using the theory of quasi-coincidence. 相似文献
6.
遗传中紧空间与散射分解 总被引:5,自引:0,他引:5
本文证明了可数仿紧(中紧、亚紧)空间有类似Junnila的刻画,遗传中紧空间不具有类似Junnila的刻画,并给出了每个散射分解有紧有限的开膨胀的充要条件. 相似文献
7.
L—Fuzzy拓扑空间中的可数F紧性与几乎可数F紧性 总被引:1,自引:0,他引:1
本文在L-uzzy拓扑空间中引入可数F紧性与几乎可数F紧性的概念,并讨论了它们的性质及其相互关系。 相似文献
8.
In several complex variables, the multivariate Padé-type approximation theory is based on the polynomial interpolation of the multidimensional Cauchy kernel and leads to complicated computations. In this paper, we replace the multidimensional Cauchy kernel by the Bergman kernel function K
(z,x) into an open bounded subset of C
n
and, by using interpolating generalized polynomials for K
(z,x), we define generalized Padé-type approximants to any f in the space OL
2() of all analytic functions on which are of class L
2. The characteristic property of such an approximant is that its Fourier series representation with respect to an orthonormal basis for OL
2() matches the Fourier series expansion of f as far as possible. After studying the error formula and the convergence problem, we show that the generalized Padé-type approximants have integral representations which give rise to the consideration of an integral operator – the so-called generalized Padé-type operator – which maps every f
OL
2() to a generalized Padé-type approximant to f. By the continuity of this operator, we obtain some convergence results about series of analytic functions of class L
2. Our study concludes with the extension of these ideas into every functional Hilbert space H and also with the definition and properties of the generalized Padé-type approximants to a linear operator of H into itself. As an application we prove a Painlevé-type theorem in C
n
and we give two examples making use of generalized Padé-type approximants. 相似文献
9.
Tsugunori Nogura 《Topology and its Applications》1983,15(1):65-69
We study the question whether a topological space X with a property can be embedded in a countably compact space X? with the same property . 相似文献
10.