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The basic theorem presented shows that the product of a linearly ordered space and a countable (regular) space is normal. We prove that the countable space can be replaced by any of a rather large class of countably tight spaces. Examples are given to prove that monotone normality cannot replace linearly ordered in the base theorem. However, it is shown that the product of a monotonically normal space and a monotonically normal countable space is normal.
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李克典 《数学物理学报(A辑)》2010,30(3):649-655
该文利用双g-函数和半连续函数给出了双层空间的刻画,得到:空间(X,Υ_1,Υ_2)是双层当且仅当对于每一个f∈Υ_i-LSC(X),都对应一个h(f)∈Υ_i-LSC(X)∩Υ_j-USC(X)使得(1)0≤h(f)≤f且当f(x)0时,0h(f)(x)f(x).(2)当f≤f′时,h(f)≤h(f′). 相似文献
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Diana G.P. Palenz 《Topology and its Applications》1982,14(2):171-182
In this paper it is proved that a topological space is necessarily paracompact if it is monotonically normal and any one of the following: screenable, paralindelöf, has a Gδ-diagonal or a quasi-Gδ-diagonal or has a σ-locally-countable base. 相似文献
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Mary Ellen Rudin Ian S. Stares Jerry E. Vaughan 《Proceedings of the American Mathematical Society》1997,125(3):927-934
We show that every countably compact space which is monotonically normal, almost 2-fully normal, radial , or with countable spread is absolutely countably compact. For the first two mentioned properties, we prove more general results not requiring countable compactness. We also prove that every monotonically normal, orthocompact space is finitely fully normal.
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Jun-ping Liang Ming He 《高等学校计算数学学报(英文版)》2006,15(4):312-319
In this paper, the totally non-positive matrix is introduced. The totally non-positive completion asks which partial totally non-positive matrices have a completion to a totally non-positive matrix. This problem has. in general, a negative answer. Therefore, our question is for what kind of labeled graphs G each partial totally non-positive matrix whose associated graph is G has a totally non-positive completion? If G is not a monotonically labeled graph or monotonically labeled cycle, we give necessary and sufficient conditions that guarantee the existence of the desired completion. 相似文献
6.
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
7.
采用K类函数法从非线性大系统集结出损失最小(相对已取得的矢量Lyapunov函数而言)的比较方程(自治非线性的),并从中取出相对简单的核方程。对后者以单调倾负曲线为脊柱构造了箱体Lyapunov函数,判定了大系统的渐近稳定性。所得判据是核方程已知量的代数显式,便于应用。 相似文献
8.
赵斌 《高校应用数学学报(英文版)》2005,20(4)
§1Introduction Theclassofstratifiable(=M3)spacesincludesallmetricspacesandmanytopological groups.Stratifiablespaceholdsmostofthestrongestandusefulpropertiesofmetric space.ThequestionproposedbyCederwhetherstratifiablespaceisM1spaceornotisstill opennow.ManyresearcheshavediscussedthepropertiesofMi(i=1,2,3)spacesthrough monotonenormality(see[2-7]).Borges[6]studiedthemonotonicallynormalproperties,Heath,etal.[5]gavemajorcontributiononmonotonenormality,andBuck,etal.[2]proposedseveraladditionalcha… 相似文献
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Zhao Bin 《高校应用数学学报(英文版)》2005,20(4):469-474
This paper investigates Buck's question about which class of spaces is strongly monotonically T2,and if other properties are combined with strongly monotonically T2,which class of spaces could be got. Based on having a cushioned pair-base space and compact strongly monotonically T2 space,some results (Theorems 1--3) are obtained. 相似文献