论文标题
Abelian晶格订购组的光谱子空间尺寸为Aleph One
Spectral subspaces of spectra of Abelian lattice-ordered groups in size aleph one
论文作者
论文摘要
It is well known that the lattice Idc G of all principal {\ell}-ideals of any Abelian {\ell}-group G is a completely normal distributive 0-lattice, and that not every completely normal distributive 0-lattice is a homomorphic image of some Idc G, via a counterexample of cardinality $\aleph 2. We prove that every completely normal distributive 0-lattice with at most $\aleph 1元素是某些IDC G的同态图像。通过石头双重性，这意味着，每个完全正常的广义光谱空间，最多具有$ \ aleph 1紧凑的开放式套件，对{\ ell} -spectrum的光谱子空间都是同型的，这些{\ ell} -spectrum的某些Abelian {\ Ell} -group的光谱子空间。
It is well known that the lattice Idc G of all principal {\ell}-ideals of any Abelian {\ell}-group G is a completely normal distributive 0-lattice, and that not every completely normal distributive 0-lattice is a homomorphic image of some Idc G, via a counterexample of cardinality $\aleph 2. We prove that every completely normal distributive 0-lattice with at most $\aleph 1 elements is a homomorphic image of some Idc G. By Stone duality, this means that every completely normal generalized spectral space, with at most $\aleph 1 compact open sets, is homeomorphic to a spectral subspace of the {\ell}-spectrum of some Abelian {\ell}-group.
