向量格与连续函数格上的序连续性和正则性
Order continuity and regularity on vector lattices and on lattices of continuous functions
AI总结：
本文刻画 Archimedean 向量格间序连续同态，借助连续函数格上的复合算子研究 $C(X)$ 子格性质，并给出正则子格刻画及 Banach 格中闭包保持正则性的结论。
摘要：
我们给出了 Archimedean 向量格之间序连续向量格同态的若干刻画。我们将某些等价性的证明归结为连续函数向量格之间复合算子的情形，从而获得了此类算子序连续性的一种刻画。受此启发，我们研究了空间 $C(X)$ 的子格的各种性质，其中 $X$ 是 Tychonoff 拓扑空间。我们还获得了向量格正则子格的若干刻画，并证明 Banach 格中正则子格的闭包也是正则的。
英文摘要：
We give several characterizations of order continuous vector lattice homomorphisms between Archimedean vector lattices. We reduce the proofs of some of the equivalences to the case of composition operators between vector lattices of continuous functions, and so we obtain a characterization of order continuity of such operators. Motivated by this, we investigate various properties of the sublattices of the space $C\left(X\right)$, where $X$ is a Tychonoff topological space. We also obtain several characterizations of a regular sublattice of a vector lattice, and show that the closure of a regular sublattice of a Banach lattice is also regular.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
