118 research outputs found
Algunas propiedades topológicas Sc-preservadas y Sc-reversibles
Tesis de Maestría que consta de un artículo de investigación que actualmente se encuentra en revisión para su publicación.El hiperespacio de las sucesiones convergentes de un espacio tipológico Hausdorff X se denota por Sc(X). Este hiperespacio es dotado de la topología de Vietoris. En este trabajo se consideran varias propiedades métrico generalizadas y se estudia la relación entre un espacio X tiene tal propiedad y su hiperespacio Sc(X) tiene la misma propiedad.Consejo Nacional de Ciencia y Tecnologí
The hyperspace of totally disconnected sets
In this paper we study the hyperspace of all nonempty closed totally disconnected subsets of a space, equipped with the Vietoris topology. We show results of compactness, connectedness and local connectedness for this hyperspace. We also include a study of path connectedness, particularly we prove that for a smooth dendroid this hyperspace is pathwise connected, and we present a general result which implies that for an Euclidean space this hyperspace has uncountably many arc components
Real extensions of distal minimal flows and continuous topological ergodic decompositions
We prove a structure theorem for topologically recurrent real skew product
extensions of distal minimal compact metric flows with a compactly generated
Abelian acting group (e.g. -flows and -flows). The main result
states that every such extension apart from a coboundary can be represented by
a perturbation of a so-called Rokhlin skew product. We obtain as a corollary
that the topological ergodic decomposition of the skew product extension into
prolongations is continuous and compact with respect to the Fell topology on
the hyperspace. The right translation acts minimally on this decomposition,
therefore providing a minimal compact metric analogue to the Mackey action.
This topological Mackey action is a distal (possibly trivial) extension of a
weakly mixing factor (possibly trivial), and it is distal if and only if
perturbation of the Rokhlin skew product is defined by a topological
coboundary.Comment: This paper is an extension and generalisation of
http://arxiv.org/abs/0909.0192. The result has been generalised from actions
of the group of integers to actions of Abelian compactly generated
transformation groups. Therefore the title had to be changed (homeomorphisms
vs. flows
A Degree of Nonlocal Connectedness
To any continuum X weassign an ordinal number (or the symbol ∞) s(X), called the degree of nonlocal connectedness of X. We show that (1) the degree cannot be increased under continuous surjections; (2) for hereditarily unicoherent continua X, the degree of a subcontinuum of X is less than or equal to s(X); (3) s(C(X)) ≤ s(X), where C(X) denotes the hyperspace of subcontinua of a continuum X. We also investigate the degrees of Cartesian products and inverse limits. As an application weconstruct an uncountable family of metric continua X homeomorphic to C(X)
Conference Program
Document provides a list of the sessions, speakers, workshops, and committees of the 32nd Summer Conference on Topology and Its Applications
Extension of Hyperspace Selections
In 1951, Ernest Michael wrote a definitive seminal article on hyperspaces
raising a general question that became known as the hyperspace selection
problem. The present paper contains some aspects of this problem, along with
several open questions. Most of these considerations and questions are related
to the usual map extension problem, but now in the setting of hyperspaces and
hyperspace selections
- …