共查询到18条相似文献,搜索用时 156 毫秒
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半连续格上的半Scott拓扑与半Lawson拓扑 总被引:4,自引:4,他引:0
在完备格上引入了半Scott拓扑与半Lawson拓扑,讨论了半连续格和强连续格上半Scott拓扑与半Lawson拓扑的一些基本性质。 相似文献
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对完备格引入半素极小集的概念,证明完备格L为半连续格当且仅当L中的每个元在L中存在半素极小集,给出半连续格的两个序同态扩张定理. 相似文献
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拓扑分子格中的半正则半开元和正则半开元 总被引:2,自引:0,他引:2
本文引入并研究了拓扑分子格中的半正则半开(半正则半闭)元和正则半开(正则半闭)元的概念。在此基础上,引入了几乎不定(几乎不定开、几乎不定闭)、几乎半连续(几乎半开、几乎半闭)和几乎半不定(几乎半不定开、几乎半不定闭)序同态的概念,同时给出了它们的若干特征性质,以及它们同其它序同态之间的关系。 相似文献
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拟半连续格和交半连续格 总被引:1,自引:0,他引:1
作为半连续格的推广, 引入了拟半连续格的概念. 讨论了拟半连续格的基本性质. 在拟半连续格上得到了类似于拟连续偏序集的一些主要结果. 同时探讨了半连续格、拟半连续格、交半连续格、交连续格、强连续格几种不同结构之间的关系. 最后,讨论了半连续函数空间仍是半连续格的条件. 相似文献
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In this article, the authors mainly study how to obtain new semicontinuous lattices from the given semicontinuous lattices and discuss the conditions under which the image of a semicontinuous projection operator is also semicontinuous. Moreover, the authors investigate the relation between semicontinuous lattices and completely distributive lattices. Finally, it is proved that the strongly semicontinuous lattice category is a Cartesian closed category. 相似文献
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The concept of `adjunct' operation of two lattices with respect to a pair of elements is introduced. A structure theorem namely,
`A finite lattice is dismantlable if and only if it is an adjunct of chains' is obtained. Further it is established that for
any adjunct representation of a dismantlable lattice the number of chains as well as the number of times a pair of elements
occurs remains the same. If a dismantlable lattice L has n elements and n+k edges then it is proved that the number of irreducible elements of L lies between n-2k-2 and n-2. These results are used to enumerate the class of lattices with exactly two reducible elements, the class of lattices with
n elements and upto n+1 edges, and their subclasses of distributive lattices and modular lattices.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
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Thomas McConville 《Order》2017,34(3):465-477
We call a finite lattice crosscut-simplicial if the crosscut complex of every nuclear interval is equal to the boundary of a simplex. Every interval of such a lattice is either contractible or homotopy equivalent to a sphere. Recently, Hersh and Mészáros introduced SB-labelings and proved that if a lattice has an SB-labeling then it is crosscut-simplicial. Some known examples of lattices with a natural SB-labeling include the join-distributive lattices, the weak order of a Coxeter group, and the Tamari lattice. Generalizing these three examples, we prove that every meet-semidistributive lattice is crosscut-simplicial, though we do not know whether all such lattices admit an SB-labeling. While not every crosscut-simplicial lattice is meet-semidistributive, we prove that these properties are equivalent for chamber posets of real hyperplane arrangements. 相似文献
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This paper characterizes those finite lattices which are a maximal sublattice of an infinite lattice. There are 145 minimal
lattices with this property, and a finite lattice has an infinite minimal extension if and only if it contains one of these
145 as a sublattice.
Received October 5, 1998; accepted in final form May 19, 1999. 相似文献
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王国俊先生于〔1〕中借助闭元成功地引入了开广义序同态的概念。本文给出了开广义序同态的一个刻划并对其是否增加拓扑分子格的权与特征等问题进行了研究,得到了积拓扑分子格的特征与权与因子拓扑分子格的特征与权间的关系,从而部分回答了LF拓扑中关于特征的两个公开问题。 相似文献
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将模糊软集的概念与格相结合,引入了(∈,∈∨q)-模糊软格和(∈,∈∨q)-模糊软格的(∈,∈∨q)-模糊软子格的概念,给出了它们的若干代数性质.定义了格的模糊软同态概念,证明了(∈,∈∨q)-模糊软格在格的一个模糊软同态下的像与原像仍为(∈,∈∨q)-模糊软格的结论. 相似文献