Asymptotically Filtered Sequences, Encasement and Boundedness
Abstract
The concept of an asymptotically filtered sequence and related notation and definitions are introduced along with the basic properties of these definitions. The companion concepts of encasement and minimal encasement, as well as several basic properties, are given in the context of finite unions of polyhedral cones. The notion of a set X being bound to another set Y, meaning every point in X is within some globally bounded distance of some point from Y, is introduced. The Chapter culminates with a characterization of X being bound to Y, assuming Y is a finite union of polyhedral cones, in terms of encasement of limits of asymptotically filtered sequences.
Publication Title
Lecture Notes in Mathematics
Recommended Citation
Grynkiewicz, D. (2022). Asymptotically Filtered Sequences, Encasement and Boundedness. Lecture Notes in Mathematics, 2316, 25-36. https://doi.org/10.1007/978-3-031-14869-9_3
