Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4658725 | Topology and its Applications | 2014 | 6 Pages |
Abstract
It is shown that several theorems known to hold in complete geodesically bounded RR-trees extend to arcwise connected Hausdorff topological spaces which have the property that every monotone increasing sequence of arcs is contained in an arc. Let X be such a space and let [u,v][u,v] denote the unique arc joining u,v∈Xu,v∈X. Among other things, it is shown and if Y is a closed connected subset of X and if f:Y→Xf:Y→X is continuous, then f has a ‘best approximation’ in Y in the sense that there exists a point z∈Yz∈Y such that [z,f(z)]∩Y={z}[z,f(z)]∩Y={z}. A set-valued analog of this result is also discussed.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
Naseer Shahzad, W.A. Kirk, Maryam A. Alghamdi,