On geometric properties of the functors of positively homogenous and semiadditive functionals
Lesya Karchevs'ka
TL;DR
This paper explores the geometric properties of functors related to positively homogenous and semiadditive functionals, establishing conditions under which their associated spaces are absolute retracts and analyzing the softness of related monad maps.
Contribution
It characterizes when the functors OH and OS produce absolute retracts and examines the conditions for the softness of multiplication maps of the generated monads.
Findings
OH(X) is AR iff X is openly generated
OS(X) is AR iff X is an openly generated compactum of weight less than ω₁
Conditions for the softness of multiplication maps of the monads
Abstract
In this paper we investigate the functors of OH of positively homogenous functionals and OS of semiadditive functionals. We show that OH(X) is AR if and only if X is openly generated, and OS(X) is AR if and only if X is an openly generated compactum of weight less than . Also, we investigate the multiplication maps of monads generated by the abovementioned functors and consider when these mappings are soft.
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 · Rings, Modules, and Algebras · Homotopy and Cohomology in Algebraic Topology