Topology of Definable Hausdorff Limits
نویسندگان
چکیده
منابع مشابه
Topology 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 کاملGeneralizations of Banach-hausdorff Limits
In a recent paper [l],1 W. F. Eberlein introduced the notion of Banach-Hausdorff limits. We employ throughout m to denote the space of all real bounded sequences [2, pp. 11 and 34]. The BanachHausdorff limits are real-valued functionals L(x), defined over m, which are Banach limits [2, p. 34], i.e., which satisfy the four conditions (i) L(ax+by)=aL(x)+bL(y) (a, b real), (ii)L(l) = l, (iii) L(x)...
متن کاملTopology of Definable Abelian Groups in O-minimal Structures
In this note we prove that every definably connected, definably compact abelian definable group G in an o-minimal expansion of a real closed field with dim(G) 6= 4 is definably homeomorphic to a torus of the same dimension. Moreover, in the semialgebraic case the result holds for all dimensions.
متن کاملA Hausdorff Topology for the Closed Subsets of a Locally Compact Non-hausdorff Space
In the structure theory of C*-algebras an important role is played by certain topological spaces X which, though locally compact in a certain sense, do not in general satisfy even the weakest separation axiom. This note is concerned with the construction of a compact Hausdorff topology for the space G(X) of all closed subsets of such a space X. This construction occurs naturally in the theory o...
متن کاملA Geometric Proof of the Definability of Hausdorff Limits
We give a geometric proof of the following well-established theorem for o-minimal expansions of the real field: the Hausdorff limits of a compact, definable family of sets are definable. While previous proofs of this fact relied on the model-theoretic compactness theorem, our proof explicitely describes the family of all Hausdorff limits in terms of the original family.
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: Discrete & Computational Geometry
سال: 2004
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-004-1112-8