$\kappa$-spaces
Saak Gabriyelyan, Evgenii Reznichenko

TL;DR
This paper introduces $ppa$-spaces, a class of Tychonoff spaces characterized by their embeddings into function spaces, and explores their stability properties, $ppa$-completion, and relationships with measures and compact subsets.
Contribution
It defines $ppa$-spaces, studies their stability, introduces the $ppa$-completion, and generalizes a result of R. Haydon regarding subspaces of Stone--zech compactifications.
Findings
$ppa$-spaces are stable under certain operations.
The $ppa$-completion $ppa X$ is the largest subspace of $eta X$ with specific properties.
Characterizations of points in $eta X$ related to measures and compactness.
Abstract
We say that a Tychonoff space is a -space if it is homeomorphic to a closed subspace of for some locally compact space . The class of -spaces is strictly between the class of Dieudonn\'{e} complete spaces and the class of -spaces. We show that the class of -spaces has nice stability properties, that allows us to define the -completion of as the smallest -space in the Stone--\v{C}ech compactification of containing . For a point , we show that (1) if , then the Dirac measure at is bounded on each compact subset of , (2) iff is continuous on each compact subset of iff is continuous on each compact subset of , (3) iff is bounded on each compact subset of…
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 Banach Space Theory · Advanced Topology and Set Theory · Rings, Modules, and Algebras
