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Lobachevskii Journal of Mathematics, vol.46, no.3, pp.1350-1356, 2025 (ESCI, Scopus)
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].