On $\mathbf{K}$-reflections of Scott spaces
General Mathematics
2022-04-21 v1
Abstract
In this paper, for a full subcategory of the category of all spaces with continuous mappings, we investigate the questions under what conditions the -reflection of a Scott space is still a Scott space and under what conditions the Scott -completion of a poset exists. Some necessary and sufficient conditions for the -reflection of a Scott space to be a Scott space and for the existence of Scott -completion of a poset are established, respectively. It is shown that neither the sobrification nor the well-filtered reflection of the Johnstone space is a Scott space. The -reflections of Alexandroff spaces and the -completions of posets are also discussed.
Cite
@article{arxiv.2204.09512,
title = {On $\mathbf{K}$-reflections of Scott spaces},
author = {Xiaoquan Xu},
journal= {arXiv preprint arXiv:2204.09512},
year = {2022}
}
Comments
16 pages, 24 references. arXiv admin note: text overlap with arXiv:1911.11618