![]() ![]() In this context, we consider the Zadeh’s extension f ^ of f to F ( X ), the family of all normal fuzzy sets on X, i.e., the hyperspace F ( X ) of all upper semicontinuous fuzzy sets on X with compact supports and non-empty levels and we endow F ( X ) with different metrics: the supremum metric d ∞, the Skorokhod metric d 0, the sendograph metric d S and the endograph metric d E. 134,Īmerican Mathematical Society, Providence, RI, 2007.Given a metric space ( X, d ), we deal with a classical problem in the theory of hyperspaces: how some important dynamical properties (namely, weakly mixing, transitivity and point-transitivity) between a discrete dynamical system f : ( X, d ) → ( X, d ) and its natural extension to the hyperspace are related. Williams, Crossed products of C ∗-algebras, Mathematical Surveys and Monographs, vol. Michael, Topologies on spaces of subsets, Trans. Kirchberg, Dini functions on spectral spaces, SFB487 preprint, nr. Fell, A Hausdorff topology for the closed subsets of a locally compact non-Hausdorff space, ![]() Dixmier, Sur les espaces localement quasi-compacts, Canad. Dixmier, C ∗-algebras, North-Holland, Amsterdam, 1977. Bourbaki, General Topology, Part 1, Elements of Mathematics, Addison-Wesley, Reading, MI, 1966. Batty, On factorial states of operator algebras, III, J. Archbold, Topologies for primal ideals, J. Clearly F ′ ( X ) = U ( ∅, converges to y as claimed. Then ( F ( X ), τ w ) is also second countable. Through all the finite subfamilies of B is a base for ( F ( X ), τ w ). If B is a base for the topology of X then the collection of all U ( ∅, Φ ) when Φ runs Lower semifinite topology in and was further discussed in. The base of a T 0 topology on F ( X ), weaker than τ s, which we shall denote by τ w. The collection of all U ( ∅, Φ ) when Φ runs through all the finite families of open subsets of X is Of course, all our results are significant only for non Hausdorff spaces, as the primitive ideal All the definitions beyond the common knowledge of a topologist or an analyst are given in the However, no knowledge of the theory of C ∗-algebras is required for the understanding of theįollowing we discuss the properties of two topologies on the collection of all the closed limit subsets of a The wealth of information given in on this class of ideals stimulated the present investigationĪnd a significant portion of the results that appear here were proved in for this special family of ideals Moreover, according to, when one restricts thisĬorrespondence to the closed limit subsets of the primitive ideal space, a very interesting class of ideals is ![]() Led Fell to the definition in of a topology on this hyperspace that is of significance in topology and Naturally, this correspondenceĪttracted the interest of operator algebraists in the hyperspace of the closed subsets of a topological space. Subsets of its primitive ideal space as detailed in. That there is a one-to-one correspondence between the closed two-sided ideals of a C ∗-algebra and the closed It seems that the modern investigation of the subject began with. The collection of all closed subsets of a topological space has been for long of interest to topologists andįunctional analysts. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |