Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8903932 | Topology and its Applications | 2018 | 26 Pages |
Abstract
A ternary relational structure ãX,[â
,â
,â
]ã, interpreting a notion of betweenness, gives rise to the family of intervals, with interval [a,b] being defined as the set of elements of X between a and b. Under very reasonable circumstances, X is also equipped with some topological structure, in such a way that each interval is a closed nonempty subset of X. The question then arises as to the continuity behavior-within the hyperspace context-of the betweenness function {x,y}â¦[x,y]. We investigate two broad scenarios: the first involves metric spaces and Menger's betweenness interpretation; the second deals with continua and the subcontinuum interpretation.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
Paul Bankston, Aisling McCluskey, Richard J. Smith,