共查询到20条相似文献,搜索用时 703 毫秒
1.
Emma D'Aniello 《Topology and its Applications》2010,157(5):954-960
Let M be the Cantor space or an n-dimensional manifold with C(M,M) the set of continuous self-maps of M, and . We prove the following:
- (1)
- If α≠∞, then Sα(M) is a nowhere dense subset of M×C(M,M) that contains no isolated points.
- (2)
- If α?β, then .
2.
Let M be a closed 5-manifold of pinched curvature 0<δ?secM?1. We prove that M is homeomorphic to a spherical space form if one of the following conditions holds:
- (i)
- The center of the fundamental group has index ?w(δ), a constant depending on δ;
- (ii)
- and the fundamental group is a non-cyclic group of order ?C, a constant;
- (iii)
- The volume is less than ?(δ) and the fundamental group is either isomorphic to a spherical 5-space group or has an odd order, and it has a center of index ?w, a constant.
3.
The main results of the paper are:
- (1)
- If X is metrizable but not locally compact topological space, then Ck(X) contains a closed copy of S2, and hence does not have the property AP;
- (2)
- For any zero-dimensional Polish X, the space Ck(X,2) is sequential if and only if X is either locally compact or the derived set X′ is compact; and
- (3)
- All spaces of the form Ck(X,2), where X is a non-locally compact Polish space whose derived set is compact, are homeomorphic, and have the topology determined by an increasing sequence of Cantor subspaces, the nth one nowhere dense in the (n+1)st.
4.
Julio Becerra Guerrero 《Journal of Functional Analysis》2008,254(8):2294-2302
We introduce representable Banach spaces, and prove that the class R of such spaces satisfies the following properties:
- (1)
- Every member of R has the Daugavet property.
- (2)
- It Y is a member of R, then, for every Banach space X, both the space L(X,Y) (of all bounded linear operators from X to Y) and the complete injective tensor product lie in R.
- (3)
- If K is a perfect compact Hausdorff topological space, then, for every Banach space Y, and for most vector space topologies τ on Y, the space C(K,(Y,τ)) (of all Y-valued τ-continuous functions on K) is a member of R.
- (4)
- If K is a perfect compact Hausdorff topological space, then, for every Banach space Y, most C(K,Y)-superspaces (in the sense of [V. Kadets, N. Kalton, D. Werner, Remarks on rich subspaces of Banach spaces, Studia Math. 159 (2003) 195-206]) are members of R.
- (5)
- All dual Banach spaces without minimal M-summands are members of R.
5.
In this paper, we show that for a convex expectation E[⋅] defined on L1(Ω,F,P), the following statements are equivalent:
- (i)
- E is a minimal member of the set of all convex expectations defined on L1(Ω,F,P);
- (ii)
- E is linear;
- (iii)
- two-dimensional Jensen inequality for E holds.
6.
Let G be a Hausdorff topological group. It is shown that there is a class C of subspaces of G, containing all (but not only) precompact subsets of G, for which the following result holds:Suppose that for every real-valued discontinuous function on G there is a set A∈C such that the restriction mapping f|A has no continuous extension to G; then the following are equivalent:
- (i)
- the left and right uniform structures of G are equivalent,
- (ii)
- every left uniformly continuous bounded real-valued function on G is right uniformly continuous,
- (iii)
- for every countable set A⊂G and every neighborhood V of the unit e of G, there is a neighborhood U of e in G such that AU⊂VA.
7.
Horst Herrlich 《Topology and its Applications》2011,158(17):2279-2286
Within the framework of Zermelo-Fraenkel set theory ZF, we investigate the set-theoretical strength of the following statements:
- (1)
- For every family(Ai)i∈Iof sets there exists a family(Ti)i∈Isuch that for everyi∈I(Ai,Ti)is a compactT2space.
- (2)
- For every family(Ai)i∈Iof sets there exists a family(Ti)i∈Isuch that for everyi∈I(Ai,Ti)is a compact, scattered, T2space.
- (3)
- For every set X, every compactR1topology (itsT0-reflection isT2) on X can be enlarged to a compactT2topology.
- (a)
- (1) implies every infinite set can be split into two infinite sets.
- (b)
- (2) iff AC.
- (c)
- (3) and “there exists a free ultrafilter” iff AC.
8.
We prove the following: Let A and B be separable C*-algebras. Suppose that B is a type I C*-algebra such that
- (i)
- B has only infinite dimensional irreducible *-representations, and
- (ii)
- B has finite decomposition rank.
0→B→C→A→0 相似文献
9.
Gabriel Padilla 《Topology and its Applications》2007,154(15):2764-2770
A classical result says that a free action of the circle S1 on a topological space X is geometrically classified by the orbit space B and by a cohomological class e∈H2(B,Z), the Euler class. When the action is not free we have a difficult open question:
- (Π)
- “Is the space X determined by the orbit space B and the Euler class?”
- •
- the intersection cohomology of X,
- •
- the real homotopy type of X.
10.
Petter Brändén 《Advances in Mathematics》2007,216(1):302-320
A polynomial f is said to have the half-plane property if there is an open half-plane H⊂C, whose boundary contains the origin, such that f is non-zero whenever all the variables are in H. This paper answers several open questions relating multivariate polynomials with the half-plane property to matroid theory.
- (1)
- We prove that the support of a multivariate polynomial with the half-plane property is a jump system. This answers an open question posed by Choe, Oxley, Sokal and Wagner and generalizes their recent result claiming that the same is true whenever the polynomial is also homogeneous.
- (2)
- We prove that a multivariate multi-affine polynomial f∈R[z1,…,zn] has the half-plane property (with respect to the upper half-plane) if and only if
11.
Mohamed Aziz Taoudi 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(1):478-3452
In this paper we prove the following Krasnosel’skii type fixed point theorem: Let M be a nonempty bounded closed convex subset of a Banach space X. Suppose that A:M→X and B:X→X are two weakly sequentially continuous mappings satisfying:
- (i)
- AM is relatively weakly compact;
- (ii)
- B is a strict contraction;
- (iii)
- .
12.
Let f,g be linearly nondegenerate meromorphic mappings of Cm into CPn. Let be hyperplanes in CPn in general position, such that
- (a)
- f−1(Hj)=g−1(Hj), for all 1?j?q,
- (b)
- dim(f−1(Hi)∩f−1(Hj))?m−2 for all 1?i<j?q, and
- (c)
- f=g on .
13.
Klaus Meer 《Discrete Mathematics》2009,309(4):843-851
We study the size of OBDDs (ordered binary decision diagrams) for representing the adjacency function fG of a graph G on n vertices. Our results are as follows:
- -
- for graphs of bounded tree-width there is an OBDD of size O(logn) for fG that uses encodings of size O(logn) for the vertices;
- -
- for graphs of bounded clique-width there is an OBDD of size O(n) for fG that uses encodings of size O(n) for the vertices;
- -
- for graphs of bounded clique-width such that there is a clique-width expression for G whose associated binary tree is of depth O(logn) there is an OBDD of size O(n) for fG that uses encodings of size O(logn) for the vertices;
- -
- for cographs, i.e. graphs of clique-width at most 2, there is an OBDD of size O(n) for fG that uses encodings of size O(logn) for the vertices. This last result complements a recent result by Nunkesser and Woelfel [R. Nunkesser, P. Woelfel, Representation of graphs by OBDDs, in: X. Deng, D. Du (Eds.), Proceedings of ISAAC 2005, in: Lecture Notes in Computer Science, vol. 3827, Springer, 2005, pp. 1132-1142] as it reduces the size of the OBDD by an O(logn) factor using encodings whose size is increased by an O(1) factor.
14.
15.
For a space X, X2 denotes the collection of all non-empty closed sets of X with the Vietoris topology, and K(X) denotes the collection of all non-empty compact sets of X with the subspace topology of X2. The following are known:
- •
- ω2 is not normal, where ω denotes the discrete space of countably infinite cardinality.
- •
- For every non-zero ordinal γ with the usual order topology, K(γ) is normal iff whenever cf γ is uncountable.
- (1)
- ω2 is strongly zero-dimensional.
- (2)
- K(γ) is strongly zero-dimensional, for every non-zero ordinal γ.
16.
Alessandro Berarducci Dikran Dikranjan Jan Pelant 《Topology and its Applications》2009,156(7):1422-1437
A metric space X is straight if for each finite cover of X by closed sets, and for each real valued function f on X, if f is uniformly continuous on each set of the cover, then f is uniformly continuous on the whole of X. A locally connected space is straight iff it is uniformly locally connected (ULC). It is easily seen that ULC spaces are stable under finite products. On the other hand the product of two straight spaces is not necessarily straight. We prove that the product X×Y of two metric spaces is straight if and only if both X and Y are straight and one of the following conditions holds:
- (a)
- both X and Y are precompact;
- (b)
- both X and Y are locally connected;
- (c)
- one of the spaces is both precompact and locally connected.
17.
S is a local maximum stable set of a graph G, and we write S∈Ψ(G), if the set S is a maximum stable set of the subgraph induced by S∪N(S), where N(S) is the neighborhood of S. In Levit and Mandrescu (2002) [5] we have proved that Ψ(G) is a greedoid for every forest G. The cases of bipartite graphs and triangle-free graphs were analyzed in Levit and Mandrescu (2003) [6] and Levit and Mandrescu (2007) [7] respectively.In this paper we give necessary and sufficient conditions for Ψ(G) to form a greedoid, where G is:
- (a)
- the disjoint union of a family of graphs;
- (b)
- the Zykov sum of a family of graphs;
- (c)
- the corona X°{H1,H2,…,Hn} obtained by joining each vertex x of a graph X to all the vertices of a graph Hx.
18.
Axel Hultman 《Journal of Combinatorial Theory, Series A》2011,118(7):1897-1906
Let W be a finite Coxeter group. For a given w∈W, the following assertion may or may not be satisfied:
- (?)
- The principal Bruhat order ideal of w contains as many elements as there are regions in the inversion hyperplane arrangement of w.
- (1)
- The criterion only involves the order ideal of w as an abstract poset. In this sense, (?) is a poset-theoretic property.
- (2)
- For W of type A, another characterisation of (?), in terms of pattern avoidance, was previously given in collaboration with Linusson, Shareshian and Sjöstrand. We obtain a short and simple proof of that result.
- (3)
- If W is a Weyl group and the Schubert variety indexed by w∈W is rationally smooth, then w satisfies (?).
19.
Tomasz Weiss 《Topology and its Applications》2008,156(1):138-141
We show that it is consistent with ZFC that there exist:
- (1)
- An unbounded (with respect to ?∗) and strongly measure zero subgroup of ZN, but without the Menger property.
- (2)
- An unbounded (with respect to ?∗) and strongly measure zero subgroup of ZN with the Menger property which does not have the Rothberger property.
20.
Let T be the class of Banach spaces E for which every weakly continuous mapping from an α-favorable space to E is norm continuous at the points of a dense subset. We show that:
- •
- T contains all weakly Lindelöf Banach spaces;
- •
- l∞∉T, which brings clarity to a concern expressed by Haydon ([R. Haydon, Baire trees, bad norms and the Namioka property, Mathematika 42 (1995) 30-42], pp. 30-31) about the need of additional set-theoretical assumptions for this conclusion. Also, (l∞/c0)∉T.
- •
- T is stable under weak homeomorphisms;
- •
- E∈T iff every quasi-continuous mapping from a complete metric space to (E,weak) is densely norm continuous;
- •
- E∈T iff every quasi-continuous mapping from a complete metric space to (E,weak) is weakly continuous at some point.