2025/07/13 by Saak Gabriyelyan, Gabriyelyan, Saak, Evgenii Reznichenko +1
Decision Sciences · Mathematics · Medicine · #Fuzzy and Soft Set Theory #Advanced Banach Space Theory #Moyamoya disease diagnosis and treatment
paper · pdf · doi:10.48550/arxiv.2507.09670
We prove that a Tychonoff space X is (sequentially) Ascoli iff for every compact space K (resp., for a convergent sequence s), each separately continuous k-continuous function Φ:X× K→ ℝ is continuous. We apply these characterizations to show that an open subspace of a (sequentially) Ascoli space is (sequentially) Ascoli, and that the μ-completion and the Dieudonné completion of a (sequentially) Ascoli space are (sequentially) Ascoli. We give also cover-type characterizations of Ascoli spaces and suggest an easy method of construction of pseudocompact Ascoli spaces which are not k_ℝ-spaces and show that each space X can be closely embedded into such a space. Using a different method we prove Hušek's theorem: a Tychonoff space Y is a locally pseudocompact k_ℝ-space iff X× Y is a k_ℝ-space for each k_ℝ-space X. It is proved that X is an s_ℝ-space iff for every locally compact sequential space K, each s-continuous function f:X× K→ℝ is continuous.