Certain Completeness Properties and Mappings
Lobachevskii Journal of Mathematics, vol.46, no.3, pp.1350-1356, 2025 (ESCI, Scopus)
- Publication Type: Article / Article
- Volume: 46 Issue: 3
- Publication Date: 2025
- Doi Number: 10.1134/s1995080224607021
- Journal Name: Lobachevskii Journal of Mathematics
- Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, zbMATH
- Page Numbers: pp.1350-1356
- Keywords: -complete, directed complete, domain representable, open map, perfect map, quotient group, topological group, Čech-complete
- Middle East Technical University Affiliated: Yes
Abstract
We prove, among the others, that the directed completeness is preserved under perfect mappings. We introduce some new notions such as nearly directed completeness, -directed completeness and directed completeness of a family. We prove that nearly directed completeness is preserved under continuous, open images and preimages with compact fibers, and consequently, we obtain that a topological group is nearly directed complete if and only if the quotient to a compact subgroup of of is nearly directed complete. We also give an upper bound for domains which improves given one in [7] and this is an answer to Question 11.10 in [3].