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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
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Kyriakos Keremedis Eleftherios Tachtsis 《Proceedings of the American Mathematical Society》2007,135(4):1205-1211
We show that the existence of a countable, first countable, zero-dimensional, compact Hausdorff space which is not second countable, hence not metrizable, is consistent with ZF.
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In the first part of this note, we mainly prove that monotone metacompactness is hereditary with respect to closed subspaces and open Fó-subspaces. For a generalized ordered (GO)-space X, we also show that X is monotonically metacompact if and only if its closed linearly ordered extension X* is monotonically metacompact. We also point out that every non-Archimedean space X is monotonically ultraparacompact. In the second part of this note, we give an alternate proof of the result that McAuley space is paracompact and metacompact. 相似文献
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Weak Covering Properties of Weak Topologies 总被引:1,自引:0,他引:1
We consider covering properties of weak topologies of Banachspaces, especially of weak or point-wise topologies of functionspaces C(K), for compact spaces K. We answer questions posedby A. V. Arkhangel'skii, S. P. Gul'ko, and R. W. Hansell. Ourmain results are the following. A Banach space of density atmost 1 is hereditarily metaLindel of in its weak topology. Ifthe weight of a compact spaceK is at most 1, then the spacesCw(K) and Cp(K) are hereditarily metaLindel of. Let be the one-point compactificationof a treeT. Then the space is hereditarily -metacompact. If T is an infinitely branchingfull tree of uncountable height and of cardinality bigger thanc, then the weak topology of the unit sphere of is not -fragmented by any metric. The space Cp(rß1)is neither metaLindel of nor -relatively metacompact. The spaceCp(rß2) is not -relatively metaLindel of. Under theset-theoretic axiom , there exists a scattered compact spaceK1 such that the space Cp(K1) is not -relatively metacompact,and under a related axiom , there exists a scattere compactspace K2 such that the space Cp(K2) is not -relatively metaLindelof. 1991 Mathematics Subject Classification: 54C35, 46B20, 54E20,54D30. 相似文献
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遗传σ-亚紧空间及其乘积性质 总被引:8,自引:0,他引:8
本文首先获得遗传σ 亚紧空间的一组等价刻划.然后,利用这组刻划得到了这类空间的两个Tychonof乘积定理以及关于σ 积的定理.最后指出:本文得到的遗传σ 亚紧空间的两个Tychonof乘积定理在σ 亚紧的情形下不成立. 相似文献
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In this paper,we present that if Y is a hereditarily metacompact space and{Xn:n∈ω}is a countable collection of Cech-scattered metacompact spaces,then the followings are∏equivalent:(1)Y×∏n∈ωXn is metacompact,(2)Y×∏n∈ωXn is countable metacompact,(3)Y×n∈ωXn is orthocompact.Thereby,this result generalizes Theorem 5.4 in[Tanaka,Tsukuba.J.Math.,1993,17:565–587].In addition,we obtain that if Y is a hereditarilyσ-metacompact space and{Xn:n∈ω∏}is a countable collection of Cech-scatteredσ-metacompact spaces,then the product Y×n∈ωXn isσ-metacompact. 相似文献
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