Abstract
A set A in a finite-dimensional Euclidean space is monovex if for any x; y ϵ A there is a continuous path within A that connects x and y and is monotone (nonincreasing or nondecreasing) in each coordinate. We prove that every open monovex set and every closed monovex set are contractible, and we provide an example of a nonopen and nonclosed monovex set that is not contractible. Our proofs reveal additional properties of monovex sets.
| Original language | English GB |
|---|---|
| Pages (from-to) | 165-178 |
| Number of pages | 14 |
| Journal | Studia Mathematica |
| Volume | 242 |
| Issue number | 2 |
| DOIs | |
| State | Published - 2018 |
Keywords
- Contractible sets
- Monovex sets
ASJC Scopus subject areas
- General Mathematics
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