1,661 research outputs found
On the second homotopy group of
In our earlier paper (K. Eda, U. Karimov, and D. Repov\v{s}, \emph{A
construction of simply connected noncontractible cell-like two-dimensional
Peano continua}, Fund. Math. \textbf{195} (2007), 193--203) we introduced a
cone-like space . In the present note we establish some new algebraic
properties of
Foliations with few non-compact leaves
Let F be a foliation of codimension 2 on a compact manifold with at least one
non-compact leaf. We show that then F must contain uncountably many non-compact
leaves. We prove the same statement for oriented p-dimensional foliations of
arbitrary codimension if there exists a closed p form which evaluates
positively on every compact leaf. For foliations of codimension 1 on compact
manifolds it is known that the union of all non-compact leaves is an open set
[A Haefliger, Varietes feuilletes, Ann. Scuola Norm. Sup. Pisa 16 (1962)
367-397].Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-12.abs.htm
Cosmic dimensions
Martin's Axiom for -centered partial orders implies that there is a
cosmic space with non-coinciding dimensions.Comment: 2005-11-15: new version, largely rewritte
Generators of von Neumann algebras associated with spectral measures
Let be the set of all values of a spectral measure and be
the smallest von Neumann algebra containing . We give a simple description
of all sets of generators of in terms of the integrals with respect to
. The treatment covers not only the case of generators belonging to
, but also the case of (possibly unbounded) generators affiliated with
this algebra.Comment: 10 pages, published versio
Universally Kuratowski-Ulam spaces and open-open games
We examine the class of spaces in which the second player has a winning
strategy in the open--open game. We show that this spaces are not universally
Kuratowski-Ulam. We also show that the games G and G7 introduced by P. Daniels,
K. Kunen, H. Zhou [Fund. Math. 145 (1994), no. 3, 205--220] are not equivalent
Covering dimension and finite-to-one maps
Hurewicz' characterized the dimension of separable metrizable spaces by means
of finite-to-one maps. We investigate whether this characterization also holds
in the class of compact F-spaces of weight c. Our main result is that, assuming
the Continuum Hypothesis, an n-dimensional compact F-space of weight c is the
continuous image of a zero-dimensional compact Hausdorff space by an at most
2n-to-1 map
Taxonomies of Model-theoretically Defined Topological Properties
A topological classification scheme consists of two ingredients: (1) an abstract class K of topological spaces; and (2) a taxonomy , i.e. a list of first order sentences, together with a way of assigning an abstract class of spaces to each sentence of the list so that logically equivalent sentences are assigned the same class.K, is then endowed with an equivalence relation, two spaces belonging to the same equivalence class if and only if they lie in the same classes prescribed by the taxonomy. A space X in K is characterized within the classification scheme if whenever Y E K, and Y is equivalent to X, then Y is homeomorphic to X. As prime example, the closed set taxonomy assigns to each sentence in the first order language of bounded lattices the class of topological spaces whose lattices of closed sets satisfy that sentence. It turns out that every compact two-complex is characterized via this taxonomy in the class of metrizable spaces, but that no infinite discrete space is so characterized. We investigate various natural classification schemes, compare them, and look into the question of which spaces can and cannot be characterized within them
-generic cocycles have one-point Lyapunov spectrum
We show the sum of the first Lyapunov exponents of linear cocycles is an
upper semicontinuous function in the topologies, for any and . This fact, together with a result from Arnold and Cong,
implies that the Lyapunov exponents of the -generic cocycle, ,
are all equal.Comment: 8 pages. A gap in the previous version was correcte
Dynamical consequences of a free interval: minimality, transitivity, mixing and topological entropy
We study dynamics of continuous maps on compact metrizable spaces containing
a free interval (i.e., an open subset homeomorphic to an open interval). A
special attention is paid to relationships between topological transitivity,
weak and strong topological mixing, dense periodicity and topological entropy
as well as to the topological structure of minimal sets. In particular, a
trichotomy for minimal sets and a dichotomy for transitive maps are proved.Comment: 21 page
On disjoint Borel uniformizations
Larman showed that any closed subset of the plane with uncountable vertical
cross-sections has aleph_1 disjoint Borel uniformizing sets. Here we show that
Larman's result is best possible: there exist closed sets with uncountable
cross-sections which do not have more than aleph_1 disjoint Borel
uniformizations, even if the continuum is much larger than aleph_1. This
negatively answers some questions of Mauldin. The proof is based on a result of
Stern, stating that certain Borel sets cannot be written as a small union of
low-level Borel sets. The proof of the latter result uses Steel's method of
forcing with tagged trees; a full presentation of this method, written in terms
of Baire category rather than forcing, is given here
- …