Upper semifinite hyperspaces as unifying tools in normal Hausdorff topology
نویسندگان
چکیده
منابع مشابه
Uniform Hyperspaces and Hausdorff Completions
We consider the uniform hyperspaces of a uniform space X, its associated Hausdorff space sX and its Hausdorff completion nX, and investigate the relationships between the functors s and n and the various hyperspace functors. Thus Theorem 1 says that there is a natural isomorphism between the functors TTE and TTETT, where ii'A'is the space of non-empty closed subsets of X, endowed with the Hausd...
متن کاملHEREDITARILY INDECOMPOSABLE HAUSDORFF CONTINUA HAVE UNIQUE HYPERSPACES 2XAND Cn(X)
Let X be a Hausdorff continuum (a compact connected Hausdorff space). Let 2X (respectively, Cn(X)) denote the hyperspace of nonempty closed subsets of X (respectively, nonempty closed subsets of X with at most n components), with the Vietoris topology. We prove that if X is hereditarily indecomposable, Y is a Hausdorff continuum and 2X (respectively Cn(X)) is homeomorphic to 2Y (respectively, C...
متن کاملHAUSDORFF HYPERSPACES OF R m AND THEIR DENSE SUBSPACES
Let BdH(R ) be the hyperspace of nonempty bounded closed subsets of Euclidean space R endowed with the Hausdorff metric. It is well known that BdH(R ) is homeomorphic to the Hilbert cube minus a point. We prove that natural dense subspaces of BdH(R ) of all nowhere dense closed sets, of all perfect sets, of all Cantor sets and of all Lebesgue measure zero sets are homeomorphic to the Hilbert sp...
متن کاملThe topology and dynamics of the hyperspaces of normal fuzzy sets and their inverse limit spaces
Given a compact and connected metric space (continuum) X, we study topological and dynamical properties of the hyperspace of normal fuzzy sets F1(X) equipped with the Hausdorff, endograph or sendograph metric. Among the many results we show that it is contractible, path connected, locally contractible, locally path connected, locally simply connected and locally connected. For the endograph met...
متن کاملTopology of Definable Hausdorff Limits
Let A ⊆ R be a set definable in an o-minimal expansion S of the real field, A′ ⊆ R be its projection, and assume that the non-empty fibers Aa ⊆ R n are compact for all a ∈ A′ and uniformly bounded. If L is the Hausdorff limit of a sequence of fibers Aai , we give an upper-bound for the Betti numbers bk(L) in terms of definable sets explicitly constructed from a generic fiber Aa. In particular, ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2007
ISSN: 0166-8641
DOI: 10.1016/j.topol.2006.03.031