TL;DR
This paper introduces the concepts of homotopical smallness and closeness, exploring their roles in homotopy theory and universal coverings, with examples, classifications, and applications.
Contribution
It defines and analyzes homotopical smallness and closeness, linking them to universal coverings and properties like homotopically Hausdorff, advancing understanding in homotopy theory.
Findings
Homotopical smallness and closeness are characterized and classified.
Connections established between these concepts and universal covering space constructions.
Applications to non-semilocally simply connected spaces and homotopically Hausdorff properties.
Abstract
The aim of this paper is to introduce the concepts of homotopical smallness and closeness. These are the properties of homotopical classes of maps that are related to recent developments in homotopy theory and to the construction of universal covering spaces for non-semilocally simply connected spaces, in particular to the properties of being homotopically Hausdorff and homotopically path Hausdorff. The definitions of notions in question and their role in homotopy theory are complemented by examples, extensional classifications, universal constructions and known applications
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.