Whitney levels in hyperspaces of non-metrizable continua
Por:
GarciaVelazquez, LM
Publicada:
1 mar 2015
Categoría:
Geometry and Topology
Resumen:
Let X be a Hausdorff continuum (a nondegenerate, compact, connected,
Hausdorff space). Let C(X) (respectively F-1 (X)) denote the hyperspace
of its subcontinua (respectively, its one-point sets), endowed with the
Vietoris topology. In this paper we introduce the definition of Whitney
levels in C(X) and discuss some basic properties. With this definition,
the subsets F-1 (X) and {X of C(X) are Whitney levels in C(X), so we
call them trivial Whitney levels. In the particular case when X is a
generalized arc, we give a condition for the existence of non-trivial
Whitney levels in its hyperspace of subcontinua. Finally, we apply this
result to the study of Whitney levels in C(X) when X is the Long Arc and
the Lexicographic Square. (C) 2015 Elsevier B.V. All rights reserved.
Filiaciones:
GarciaVelazquez, LM:
Univ Nacl Autonoma Mexico, Inst Matemat, Area Invest Cient, Mexico City 04510, DF, Mexico
|