Đã lưu trong:
| Tác giả chính: | |
|---|---|
| Định dạng: | Preprint |
| Được phát hành: |
2021
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| Những chủ đề: | |
| Truy cập trực tuyến: | https://arxiv.org/abs/2103.08776 |
| Các nhãn: |
Thêm thẻ
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Mục lục:
- 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.