Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 12

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last

Wyniki wyszukiwania

help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Content available remote

On $\check{H}^n$-bubbles in n-dimensional compacta

100%
Karimov U. H., Repovš D.
Colloquium Mathematicum
|
1998
|
tom 75
|
nr 1
39-51
EN
A topological space X is called an $\check{H}^n$-bubble (n is a natural number, $\check{H}^n$ is Čech cohomology with integer coefficients) if its n-dimensional cohomology $\check{H}^n(X)$ is nontrivial and the n-dimensional cohomology of every proper subspace is trivial. The main results of our paper are: (1) Any compact metrizable $\check{H}^n$-bubble is locally connected; (2) There exists a 2-dimensional 2-acyclic compact metrizable ANR which does not contain any $\check{H}^2$-bubbles; and (3) Every n-acyclic finite-dimensional $L\check{H}^n$-trivial metrizable compactum contains an $\check{H}^n$-bubble.
2
Content available remote

Nonlinear mappings preserving at least one eigenvalue

100%
Costara C., Repovš D.
Studia Mathematica
|
2010
|
tom 200
|
nr 1
79-89
EN
We prove that if F is a Lipschitz map from the set of all complex n × n matrices into itself with F(0) = 0 such that given any x and y we know that F(x) - F(y) and x-y have at least one common eigenvalue, then either $F(x) = uxu^{-1}$ or $F(x) = ux^{t}u^{-1}$ for all x, for some invertible n × n matrix u. We arrive at the same conclusion by supposing F to be of class 𝓒¹ on a domain in ℳₙ containing the null matrix, instead of Lipschitz. We also prove that if F is of class 𝓒¹ on a domain containing the null matrix satisfying F(0) = 0 and ρ(F(x) - F(y)) = ρ(x-y) for all x and y, where ρ(·) denotes the spectral radius, then there exists γ ∈ ℂ of modulus one such that either $γ^{-1}F$ or $γ^{-1}F̅$ is of the above form, where F̅ is the (complex) conjugate of F.
3
Content available remote

Cell-like resolutions of polyhedra by special ones

100%
Repovš D., Skopenkov A.
Colloquium Mathematicum
|
2000
|
tom 86
|
nr 2
231-237
EN
Suppose that P is a finite 2-polyhedron. We prove that there exists a PL surjective map f:Q → P from a fake surface Q with preimages of f either points or arcs or 2-disks. This yields a reduction of the Whitehead asphericity conjecture (which asserts that every subpolyhedron of an aspherical 2-polyhedron is also aspherical) to the case of fake surfaces. Moreover, if the set of points of P having a neighbourhood homeomorphic to the 2-disk is a disjoint union of open 2-disks, and every point of P has an arbitrarily small 2-dimensional neighbourhood, then we may additionally conclude that Q is a special 2-polyhedron.
4
Content available remote

Classifying homogeneous ultrametric spaces up to coarse equivalence

100%
Banakh T., Repovš D.
Colloquium Mathematicum
|
2016
|
tom 144
|
nr 2
189-202
EN
For every metric space X we introduce two cardinal characteristics $cov^{♭}(X)$ and $cov^{♯}(X)$ describing the capacity of balls in X. We prove that these cardinal characteristics are invariant under coarse equivalence, and that two ultrametric spaces X,Y are coarsely equivalent if $cov^{♭}(X) = cov^{♯}(X) = cov^{♭}(Y) = cov^{♯}(Y)$. This implies that an ultrametric space X is coarsely equivalent to an isometrically homogeneous ultrametric space if and only if $cov^{♭}(X) = cov^{♯}(X)$. Moreover, two isometrically homogeneous ultrametric spaces X,Y are coarsely equivalent if and only if $cov^{♯}(X) = cov^{♯}(Y)$ if and only if each of them coarsely embeds into the other. This means that the coarse structure of an isometrically homogeneous ultrametric space X is completely determined by the value of the cardinal $cov^{♯}(X) = cov^{♭}(X)$.
5
Content available remote

On the homology of the Harmonic Archipelago

100%
Karimov U., Repovš D.
Open Mathematics
|
2012
|
tom 10
|
nr 3
863-872
EN
We calculate the singular homology and Čech cohomology groups of the Harmonic Archipelago. As a corollary, we prove that this space is not homotopy equivalent to the Griffiths space. This is interesting in view of Eda’s proof that the first singular homology groups of these spaces are isomorphic.
6
Content available remote

Detecting codimension one manifold factors with the piecewise disjoint arc-disk property and related properties

100%
Halverson D., Repovš D.
Open Mathematics
|
2013
|
tom 11
|
nr 11
1932-1948
EN
We show that all finite-dimensional resolvable generalized manifolds with the piecewise disjoint arc-disk property are codimension one manifold factors. We then show how the piecewise disjoint arc-disk property and other general position properties that detect codimension one manifold factors are related. We also note that in every example presently known to the authors of a codimension one manifold factor of dimension n ≥ 4 determined by general position properties, the piecewise disjoint arc-disk property is satisfied.
7
Content available remote

On manifold spines and cyclic presentations of groups

81%
Cavicchioli A., Hegenbarth F., Repovš D.
Banach Center Publications
|
1998
|
tom 42
|
nr 1
49-56
EN
This is a survey of results and open problems on compact 3-manifolds which admit spines corresponding to cyclic presentations of groups. We also discuss questions concerning spines of knot manifolds and regular neighborhoods of homotopically PL embedded compacta in 3-manifolds.
8
Content available remote

On uncountable collections of continua and their span

81%
Repovš D., Skopenkov A. B., Ščepin E. V.
Colloquium Mathematicum
|
1996
|
tom 69
|
nr 2
289-296
EN
We prove that if the Euclidean plane $ℝ^2$ contains an uncountable collection of pairwise disjoint copies of a tree-like continuum X, then the symmetric span of X is zero, sX = 0. We also construct a modification of the Oversteegen-Tymchatyn example: for each ε > 0 there exists a tree $X ⊂ ℝ^2$ such that σX < ε but X cannot be covered by any 1-chain. These are partial solutions of some well-known problems in continua theory.
9
Content available remote

On manifolds with nonhomogeneous factors

81%
Cárdenas M., Lasheras F., Quintero A., Repovš D.
Open Mathematics
|
2012
|
tom 10
|
nr 3
857-862
EN
We present simple examples of finite-dimensional connected homogeneous spaces (they are actually topological manifolds) with nonhomogeneous and nonrigid factors. In particular, we give an elementary solution of an old problem in general topology concerning homogeneous spaces.
10
Content available remote

Countable dense homogeneous filters and the Menger covering property

81%
Repovš D., Zdomskyy L., Zhang S.
Fundamenta Mathematicae
|
2014
|
tom 224
|
nr 3
233-240
EN
We present a ZFC construction of a non-meager filter which fails to be countable dense homogeneous. This answers a question of Hernández-Gutiérrez and Hrušák. The method of the proof also allows us to obtain for any n ∈ ω ∪ {∞} an n-dimensional metrizable Baire topological group which is strongly locally homogeneous but not countable dense homogeneous.
11
Content available remote

A construction of noncontractible simply connected cell-like two-dimensional Peano continua

81%
Eda K., Karimov U., Repovš D.
Fundamenta Mathematicae
|
2007
|
tom 195
|
nr 3
193-203
EN
Using the topologist sine curve we present a new functorial construction of cone-like spaces, starting in the category of all path-connected topological spaces with a base point and continuous maps, and ending in the subcategory of all simply connected spaces. If one starts from a noncontractible n-dimensional Peano continuum for any n > 0, then our construction yields a simply connected noncontractible (n + 1)-dimensional cell-like Peano continuum. In particular, starting from the circle 𝕊¹, one gets a noncontractible simply connected cell-like 2-dimensional Peano continuum.
12
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
Content available

The recognition problem for topological manifolds

69%
Repovš D.
Banach Center Publications
|
1986
|
tom 18
|
nr 1
77-108
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.