Balibrea, Francisco; Valverde Fajardo, Jose C.
[EN] This paper is devoted to study the topological normal forms of families of maps on R which, under nondegeneracy conditions of high degree, also present the simplest bifurcations.
Kennedy, Judy A.; Kopperman, Ralph D.; Wilson, Richard G.
[EN] We show that the chainable continua (also called snake-like or arc-like)continua, are precisely the Hausdorff reflections of inverse limits of sequences of finite COTS under maps which are continuous and are separating.
Chasco, M. J.; Martin-Peinador, E.
[EN] An Abelian topological group G is strongly reflexive if every closed subgroup and every Hausdorff quotient of G and of its dual group G⋀, is reflexive. In this paper we prove the following: the annihilator of a closed subgroup of an almost metrizable group is topologically isomorphic to the dual of the corresponding Hausdorff quotient, and an analogous statement holds for the character group of the starting group. As a consequence of this perfect duality, an almost metrizable group is strongly reflexive just if its Hausdorff quotients, as well as the Hausdorff quotients of its dual, are reflexive. The...
Cao, Jiling; Greenwood, Sina; Reilly, Ivan L.
[EN] We investigate various classes of generalized closed sets of a topological space in a unified way by studying the notion of qr-closed sets. New characterizations of some existing classes of generalized closed sets and topological spaces are given. A new class of generalized closed sets are introduced.
Arenas, F.G.; Sánchez Granero, M.A.
[EN] In this paper we introduce the concept of directed fractal structure, which is a generalization of the concept of fractal structure (introduced by the authors). We study the relation with transitive quasiuniformities and inverse limits of posets. We define the concept of GF-compactification and apply it to prove that the Stone-Cech compactification can be obtained as the GF-compactification of the directed fractal structure associated to the Pervin quasi-uniformity.
[EN] The Bohr topology of an Abelian group G is the initial topology on G with respect to the family of all homomorphisms of G into the circle group. The group G equipped with the Bohr topology is denoted by G#. It was an open question of van Douwen whether for any two discrete abelian groups G and H of the same cardinality the topological spaces G# and H# are homeomorphic. A negative solution to van Douwen's problem was given independently by Kunen and by Watson and the authot. In both cases infinite dimensional vector spaces Vp over the finite...