Baire and weakly Namioka spaces
Zbigniew Piotrowski, Russell Waller

TL;DR
This paper explores the relationship between Baire and weakly Namioka spaces, establishing conditions under which they coincide in certain classes of topological spaces.
Contribution
It introduces the concept of weakly Namioka spaces and proves their equivalence to Baire spaces within specific classes of topological spaces.
Findings
Weakly Namioka spaces are characterized by a modified Namioka condition with second countability.
In completely regular separable and perfectly normal spaces, Baire and weakly Namioka spaces are equivalent.
Abstract
Recall that a Hausdorff space is said to be Namioka if for every compact (Hausdorff) space and every metric space , every separately continuous function is continuous on for some dense subset of . It is well known that in the class of all metrizable spaces, Namioka and Baire spaces coincide (Saint-Raymond, 1983). Further it is known that every completely regular Namioka space is Baire and that every separable Baire space is Namioka (Saint-Raymond, 1983). In our paper we study spaces , we call them weakly Namioka, for which the conclusion of the theorem for Namioka spaces holds provided that the assumption of compactness of is replaced by second countability of . We will prove that in the class of all completely regular separable spaces and in the class of all perfectly normal spaces, is Baire if and…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Topology and Set Theory · Advanced Banach Space Theory · Fuzzy and Soft Set Theory
