Certain Completeness Properties and Mappings
Lobachevskii Journal of Mathematics, cilt.46, sa.3, ss.1350-1356, 2025 (ESCI, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 46 Sayı: 3
- Basım Tarihi: 2025
- Doi Numarası: 10.1134/s1995080224607021
- Dergi Adı: Lobachevskii Journal of Mathematics
- Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, zbMATH
- Sayfa Sayıları: ss.1350-1356
- Anahtar Kelimeler: -complete, directed complete, domain representable, open map, perfect map, quotient group, topological group, Čech-complete
- Orta Doğu Teknik Üniversitesi Adresli: Evet
Özet
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].