ISSN:
1572-9168
Keywords:
Primary 52.A30
;
52.A10
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Let S be a subset of R d . The set S is said to be an ℒ set if and only if for every two points x and y of S, there exists some z ∈ S such that [x, z] ⋃ [z, y] ⊂ S. Clearly every starshaped set is an ℒ set, yet the converse is false and introduces an interesting question: ‘Under what conditions will an ℒ set S be “almost” starshaped; that is, when will there exist a convex subset C of S such that every point of S sees some point of C via S’ This paper provides one answer to the question above, and we have the following result: Let S be a closed planar ℒ set, S simply connected, and assume that the set Q of points of local nonconvexity of S is finite. If some point p of S see each member of Q via S, then there is a convex subset C of S such that every point of S sees some point of C via S.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00147785
