Connectivity and homology of finite subset spaces of cardinality at most four
نویسندگان
چکیده
منابع مشابه
some properties of fuzzy hilbert spaces and norm of operators
in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...
15 صفحه اولConnectivity of Finite Subset Spaces of Cell Complexes
The k-th finite subset space of a topological space X is the space expkX of nonempty subsets of X of size at most k, topologised as a quotient of X. Using results from our earlier paper on the finite subset spaces of connected graphs we show that the k-th finite subset space of a connected cell complex is (k − 2)-connected, and (k − 1)-connected if in addition the underlying space is simply con...
متن کاملRemarks on Finite Subset Spaces
This paper expands on and refines some known and less well-known results about the finite subset spaces of a simplicial complex X including their connectivity and manifold structure. It also discusses the inclusion of the singletons into the threefold subset space and shows that this subspace is weakly contractible but generally non-contractible unless X is a cogroup. Some homological calculati...
متن کاملFinite subset spaces of S 1
Given a topological space X denote by expkX the space of non-empty subsets of X of size at most k , topologised as a quotient of X . This space may be regarded as a union over 1 ≤ l ≤ k of configuration spaces of l distinct unordered points in X . In the special case X = S we show that: (1) expkS 1 has the homotopy type of an odd dimensional sphere of dimension k or k − 1; (2) the natural inclu...
متن کاملFinite subset spaces of closed surfaces
The kth finite subset space of a topological space X is the space expkX of non-empty finite subsets of X of size at most k , topologised as a quotient of X . The construction is a homotopy functor and may be regarded as a union of configuration spaces of distinct unordered points in X . We show that the finite subset spaces of a connected 2–complex admit “lexicographic cell structures” based on...
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: 2011
ISSN: 0166-8641
DOI: 10.1016/j.topol.2011.05.034