Autor: Repovš, Dušan - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Cell-like resolutions of polyhedra by special ones
Autorzy:: Repovš, Dušan
Skopenkov, Arkady
Powiązania:: https://bibliotekanauki.pl/articles/965832.pdf
Data publikacji:: 2000
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: banana and pineapple trick
cell-like resolution
Whitehead conjecture
special polyhedron
fake surface
Opis:: 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.
Źródło:: Colloquium Mathematicum; 2000, 86, 2; 231-237
0010-1354
Pojawia się w:: Colloquium Mathematicum
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: On $\check{H}^n$-bubbles in n-dimensional compacta
Autorzy:: Karimov, Umed
Repovš, Dušan
Powiązania:: https://bibliotekanauki.pl/articles/1396055.pdf
Data publikacji:: 1998
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: locally connected spaces
low-dimensional compacta
Čech cohomology
bubble
slender group
Opis:: 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.
Źródło:: Colloquium Mathematicum; 1998, 75, 1; 39-51
0010-1354
Pojawia się w:: Colloquium Mathematicum
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: On uncountable collections of continua and their span
Autorzy:: Repovš, Dušan
Skopenkov, Arkadij
Ščepin, Evgenij
Powiązania:: https://bibliotekanauki.pl/articles/967010.pdf
Data publikacji:: 1996
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: uncountable collection of compacta
deleted product
chainable continua
span
equivariant maps
symmetric span
Opis:: 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.
Źródło:: Colloquium Mathematicum; 1996, 69, 2; 289-296
0010-1354
Pojawia się w:: Colloquium Mathematicum
Dostawca treści:: Biblioteka Nauki

Artykuł

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